"Over 80% of the brain's neurons are located in the cerebellum."
It sounds counterintuitive, but the tiny cerebellum — that dense, cauliflower-like structure tucked at the back of the skull — holds the vast majority of the brain's neurons, and the numbers back it up.
What Was Claimed?
The claim is that more than 80% of all the neurons in the human brain are packed into the cerebellum. Most people think of the cerebrum — the large, wrinkled outer brain — as the "main" brain, so the idea that a structure accounting for just 10% of the brain's weight could house over four-fifths of its cells strikes many as surprising, or even implausible. Understanding where neurons actually live matters for anyone thinking about how the brain processes movement, learning, or disease.
What Did We Find?
The numbers come from a landmark 2009 study published in Frontiers in Human Neuroscience by neuroscientist Suzana Herculano-Houzel, who used a method called isotropic fractionation to count neurons directly rather than estimating from volume. Her data: the human brain contains roughly 86 billion neurons in total, and 69 billion of those are in the cerebellum. That works out to 80.23% — just barely over the 80% mark.
Two independent peer-reviewed papers corroborate the figure. A 2016 review of 150 years of cell-counting methodology in the Journal of Comparative Neurology states plainly that "the cerebellum contains about 80% of all neurons in the human brain." A separate 2010 cross-species study by Herculano-Houzel and colleagues, comparing everything from mice to macaques to humans, also places the human figure at 80%.
The reason for the discrepancy between the cerebellum's modest size and its enormous neuron count is density. Cerebellar granule cells are among the smallest and most tightly packed neurons in the nervous system. The cerebrum is bigger and more metabolically demanding per neuron, but it is far less densely packed. Volume and neuron count simply don't track each other the way most people assume.
What Should You Keep In Mind?
The margin here is thin. The computed value is 80.23% — just 0.23 percentage points above the 80% threshold. The original study reports measurement uncertainties of roughly ±8 billion for total neurons and ±6.6 billion for cerebellar neurons, which are much larger than that margin. The scientific literature consistently describes the figure as "about 80%," not "strictly over 80%." The claim is proved on the point estimates as reported, but treating it as a precise hard fact rather than an approximate one would be a mistake.
There is also a competing measurement. A 2013 study by Andrade-Moraes and colleagues, using a different methodology, estimated only 54 billion cerebellar neurons — which would place the cerebellum at around 63% of total neurons, well below 80%. That study hasn't displaced the Azevedo/Herculano-Houzel count as the field's reference figure, but it is a real scientific alternative, not noise.
One definitional point matters: "brain" here means the organ inside the skull — cerebrum, cerebellum, and brainstem — and excludes the spinal cord. If you include the spinal cord's roughly 1 billion neurons, the cerebellum's share drops to about 79.3%, just under 80%. The claim is true under standard neuroanatomical usage.
How Was This Verified?
This claim was evaluated by fetching the cited sources live, extracting neuron counts directly from quoted text, computing the percentage independently, and cross-checking the result against two separately authored peer-reviewed papers. You can read the full breakdown in the structured proof report, inspect every citation and computation step in the full verification audit, or re-run the proof yourself.
What could challenge this verdict?
1. Competing methodology (Andrade-Moraes et al. 2013): The PMC5063692 review (Table 4) lists an alternative estimate of 54 billion cerebellar neurons from Andrade-Moraes et al. (2013) — 22% lower than Azevedo's 69 billion. Using 54B of an assumed 86B total yields ~62.8%, well below 80%. This is a genuine methodological dispute. However, Azevedo et al. 2009's isotropic fractionation method is the current gold standard and is cited universally in reviews and neuroscience education. No peer-reviewed paper argues the cerebellum holds ≤80% under the Azevedo methodology.
2. Popular-science understatement: brainfacts.org (2020) states the cerebellum contains "more than half of its neurons" — a much lower claim. This is a popular-science source, not a peer-reviewed estimate, and does not contradict the quantitative finding.
3. Spinal cord inclusion: The human spinal cord contains ~1 billion neurons. Including it raises the total to ~87 billion: 69/87 = 79.3%, just below 80%. However, "brain" in neuroanatomy excludes the spinal cord by definition, and all cited sources use this convention.
4. Thin margin (0.23 pp): The computed excess over 80% is only 0.23 percentage points. Azevedo et al. 2009 report uncertainty of ±8.1B for total neurons and ±6.65B for cerebellum neurons — the margin is within measurement error. The scientific literature consistently rounds to "about 80%" without claiming strictly greater. This is a genuine limitation: the proof rests on point estimates, not a confidently strict threshold. The verdict is PROVED on the point estimates as reported, with this caveat noted.
5. Linguistic interpretation: "Over 80%" means > 80.0% in standard English. The computed 80.23% satisfies this.
Sources
| Source | ID | Type | Verified |
|---|---|---|---|
| Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31. PMC2776484 | B1 | Government | Yes |
| Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31. PMC2776484 | B2 | Government | Yes |
| von Bartheld CS, Bahney J, Herculano-Houzel S (2016) The search for true numbers of neurons and glial cells in the human brain. J Comp Neurol 524(18):3865-3895. PMC5063692 | B3 | Government | Yes |
| Herculano-Houzel S, Catania K, Manger PR, Kaas JH (2010) Coordinated scaling of cortical and cerebellar numbers of neurons. Front Neuroanat 4:12 | B4 | Academic | Yes |
| Computed cerebellum neuron %: (69 billion / 86 billion) × 100 | A1 | — | Computed |
detailed evidence
Evidence Summary
| ID | Fact | Verified |
|---|---|---|
| B1 | Total human brain neuron count: 86 billion — Herculano-Houzel 2009 (PMC2776484) | Yes |
| B2 | Cerebellum neuron count: 69 billion — Herculano-Houzel 2009 (PMC2776484) | Yes |
| B3 | Independent statement: cerebellum ~80% of brain neurons — von Bartheld et al. 2016 review (PMC5063692) | Yes |
| B4 | Cross-species comparison: 80% in human — Herculano-Houzel et al. 2010 Frontiers Neuroanatomy | Yes |
| A1 | Computed cerebellum neuron %: (69B / 86B) × 100 = 80.23% | Computed |
Source: proof.py JSON summary
Proof Logic
The primary neuron counts come from Herculano-Houzel (2009), a peer-reviewed review in Frontiers in Human Neuroscience (PMC2776484) that synthesizes the landmark isotropic fractionation study by Azevedo et al. (2009):
- Total brain neurons (B1): 86 billion — parsed from the quote "the adult male human brain, at an average of 1.5 kg, has 86 billion neurons and 85 billion non-neuronal cells"
- Cerebellum neurons (B2): 69 billion — parsed from "the human cerebellum, at 154 g and 69 billion neurons, matches or even slightly exceeds the expected"
Both data values ("86 billion neurons", "69 billion neurons") were confirmed to appear verbatim on the live page.
The computed percentage (A1):
69,000,000,000 / 86,000,000,000 × 100 = 80.2326%
This exceeds the 80% threshold, so the claim holds: SC1 (80.23% > 80%) = True.
Two independent sources corroborate this figure:
- B3 (von Bartheld et al. 2016, PMC5063692) — a major review of 150 years of cell-counting methodology — states: "the cerebellum (which contains about 80% of all neurons in the human brain; Azevedo et al. (2009))"
- B4 (Herculano-Houzel et al. 2010, Frontiers Neuroanatomy) — a cross-species comparative study — states: "the cerebellum holds … 80% in the agouti, galago, and human"
Both independently agree within 2 percentage points of the computed 80.23% (cross-check tolerance satisfied).
Conclusion
Verdict: PROVED
The human cerebellum contains 69 billion of the brain's 86 billion neurons — 80.23% — which is strictly greater than 80%, as confirmed by: - Live-verified raw counts from a peer-reviewed PMC source (B1, B2) - Two independent peer-reviewed sources stating "80%" (B3, B4) - All four citations fully verified (tier 4–5 sources)
Important caveat: The margin is thin (0.23 pp), and the measurement uncertainty in the underlying Azevedo et al. 2009 study (±8–9% on neuron counts) is larger than this margin. The scientific literature consistently characterizes the figure as "about 80%" rather than "strictly over 80%." Under the dominant methodology the claim is TRUE, but a competing estimate (Andrade-Moraes 2013) yields ~63%, which would disprove it.
audit trail
All 4 citations verified.
Original audit log
B1 — Herculano-Houzel 2009 (PMC2776484) — total neurons - Status: verified - Method: full_quote - Fetch mode: live - Data values confirmed: "86 billion neurons" found on page [live]
B2 — Herculano-Houzel 2009 (PMC2776484) — cerebellum neurons - Status: verified - Method: full_quote - Fetch mode: live - Data values confirmed: "69 billion neurons" found on page [live]
B3 — von Bartheld et al. 2016 (PMC5063692) - Status: verified - Method: full_quote - Fetch mode: live
B4 — Herculano-Houzel et al. 2010 (Frontiers Neuroanatomy) - Status: verified - Method: full_quote - Fetch mode: live
Source: proof.py inline output (execution trace)
| Field | Value |
|---|---|
| Subject | Human cerebellum |
| Property | Percentage of total brain neurons located in the cerebellum |
| Operator | > |
| Threshold | 80.0% |
| Operator note | "'Over 80%' is interpreted as strictly greater than 80.0%. If the cerebellum held exactly 80.0% of neurons the claim would be FALSE. 'Brain' means the entire brain (cerebrum + cerebellum + brainstem) excluding the spinal cord — the standard neuroanatomical usage in all cited sources. The more conservative strict-greater-than reading is used; >= would make the claim easier to prove." |
Source: proof.py JSON summary
Natural language: Over 80% of the brain's neurons are located in the cerebellum.
Formal interpretation:
| Field | Value |
|---|---|
| Subject | Human cerebellum |
| Property | Percentage of total brain neurons in the cerebellum |
| Operator | > (strictly greater than) |
| Threshold | 80.0% |
Operator rationale: "Over 80%" is interpreted as strictly greater than 80.0%. If the cerebellum held exactly 80.0%, the claim would be FALSE. This is the more conservative reading; using ≥ would make the claim easier to prove. "Brain" means the entire brain (cerebrum + cerebellum + brainstem) excluding the spinal cord — the standard neuroanatomical usage in all cited sources.
| Fact ID | Domain | Type | Tier | Note |
|---|---|---|---|---|
| B1 | nih.gov | government | 5 | Government domain (.gov) — PubMed Central |
| B2 | nih.gov | government | 5 | Government domain (.gov) — PubMed Central |
| B3 | nih.gov | government | 5 | Government domain (.gov) — PubMed Central |
| B4 | frontiersin.org | academic | 4 | Known academic/scholarly publisher |
All citations tier 4 or 5. No low-credibility sources cited.
Source: proof.py JSON summary
=== Verifying citations ===
[✓] source_a_total: Full quote verified for source_a_total (source: tier 5/government)
[✓] source_a_cerebellum: Full quote verified for source_a_cerebellum (source: tier 5/government)
[✓] source_b: Full quote verified for source_b (source: tier 5/government)
[✓] source_c: Full quote verified for source_c (source: tier 4/academic)
=== Verifying data values ===
[✓] B1.total_neurons: '86 billion neurons' found on page [live]
[✓] B2.cerebellum_neurons: '69 billion neurons' found on page [live]
[✓] B1: extracted 86 from quote
[✓] B2: extracted 69 from quote
Extracted total brain neurons: 86 billion
Extracted cerebellum neurons: 69 billion
=== Computation ===
Cerebellum % of total brain neurons: cerebellum_neurons / total_neurons * 100 = 69000000000.0 / 86000000000.0 * 100 = 80.2326
=== Claim Evaluation ===
SC1: cerebellum neuron % > 80%: 80.23255813953489 > 80.0 = True
=== Cross-check ===
[✓] B3: extracted 80 from quote
Computed 80.23% vs B3 stated ~80% (von Bartheld 2016): 80.23255813953489 vs 80.0, diff=0.2325581395348877, tolerance=2.0 -> AGREE
[✓] B4: extracted 80 from quote
Computed 80.23% vs B4 stated 80% (Herculano-Houzel 2010): 80.23255813953489 vs 80.0, diff=0.2325581395348877, tolerance=2.0 -> AGREE
Source: proof.py inline output (execution trace)
| Cross-check | Values | Tolerance | Mode | Agreement |
|---|---|---|---|---|
| Computed 80.23% vs B3 stated ~80% (von Bartheld 2016 review) | 80.2326 vs 80.0 | 2.0 pp | absolute | Yes (diff = 0.23 pp) |
| Computed 80.23% vs B4 stated 80% (Herculano-Houzel 2010) | 80.2326 vs 80.0 | 2.0 pp | absolute | Yes (diff = 0.23 pp) |
Note on independence: B1 and B2 share the same URL (PMC2776484) — they are the same published paper but carry two distinct facts (total count and cerebellum count). B3 (PMC5063692) and B4 (Frontiers 2010) are independently authored papers that state the 80% figure, providing independent source agreement with the computed value. This constitutes "independently published (same upstream authority — Azevedo 2009)" rather than fully independent measurements.
Source: proof.py JSON summary
1. Does any peer-reviewed source dispute the ~80% figure? - Verification: Searched "cerebellum percentage brain neurons 80 percent counter-evidence dispute". Found brainfacts.org (2020) says "more than half." Found PMC5063692 Table 4 lists Andrade-Moraes 2013 at 54×10⁹ cerebellum neurons vs Azevedo's 69×10⁹. - Finding: Andrade-Moraes 2013 is a genuine alternative giving ~63% under the same total — well below 80%. brainfacts.org is popular science. No peer-reviewed paper disputes ~80% under the Azevedo methodology. - Breaks proof: No
2. If 'brain' included the spinal cord, would the percentage fall below 80%? - Verification: Searched spinal cord neuron count. Estimate: ~1 billion. 69/(86+1) = 79.3%. - Finding: Yes, it would drop to 79.3%. But "brain" excludes the spinal cord by standard neuroanatomical definition used in all cited sources. - Breaks proof: No
3. Is the margin of 0.23 pp within measurement error? - Verification: Azevedo 2009 reports 86.1 ± 8.1B total and 69.03 ± 6.65B cerebellum. Lower-bound ratio: 66.2%; upper: 97.0%. - Finding: The 0.23 pp excess is within measurement uncertainty. The proof rests on point estimates. Scientific literature says "about 80%," not "strictly over 80%." Genuine limitation noted; does not disprove the claim. - Breaks proof: No
4. Could 'over 80%' linguistically require 81%+? - Verification: Linguistic analysis. - Finding: "Over 80%" means > 80.0% in standard English. 80.23% satisfies this. - Breaks proof: No
Source: proof.py JSON summary
- [x] Rule 1: All values parsed from quote text using regex +
verify_extraction(). No hand-typed numbers. - [x] Rule 2: All 4 citation URLs fetched live; all quotes verified (full_quote method).
- [x] Rule 3: N/A — no date-dependent computations in this proof.
- [x] Rule 4:
CLAIM_FORMALwithoperator_notedocuments the strict-greater-than interpretation and definition of "brain." - [x] Rule 5: Adversarial checks searched for counter-evidence (Andrade-Moraes competing estimate, spinal cord inclusion, measurement uncertainty, brainfacts.org understatement).
- [x] Rule 6: Cross-checks use B3 and B4 as independently authored sources to corroborate the computed percentage. B1/B2 share a URL but carry distinct factual claims. Independence note documented.
- [x] Rule 7: No hard-coded constants.
explain_calc()andcompare()used fromscripts/computations.py. - [x] validate_proof.py: 14/14 checks passed, 0 issues, 0 warnings — STATUS: PASS
| ID | Extracted Value | Found in Quote | Quote Snippet |
|---|---|---|---|
| B1 | 86 billion (86,000,000,000) | Yes | "the adult male human brain, at an average of 1.5 kg, has 86 billion neurons and…" |
| B2 | 69 billion (69,000,000,000) | Yes | "the human cerebellum, at 154 g and 69 billion neurons, matches or even slightly…" |
| B3 | 80% | Yes | "the cerebellum (which contains about 80% of all neurons in the human brain; Azev…" |
| B4 | 80% | Yes | "the cerebellum holds 60% of all brain neurons in the mouse, small shrews, and ma…" |
Extraction method for B1/B2: Regex (\d+) billion neurons applied after normalize_unicode(). Integer captured, then multiplied by 10⁹. verify_extraction() confirms the raw integer (86, 69) appears in the original quote string.
Extraction method for B3: Regex about (\d+)% applied after normalize_unicode(). Captured 80.
Extraction method for B4: Regex and (\d+)% in the agouti applied after normalize_unicode(). Captured 80.
Source: proof.py JSON summary; extraction method description is author analysis
Cite this proof
Proof Engine. (2026). Claim Verification: “Over 80% of the brain's neurons are located in the cerebellum.” — Proved. https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/
Proof Engine. "Claim Verification: “Over 80% of the brain's neurons are located in the cerebellum.” — Proved." 2026. https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/.
@misc{proofengine_over_80_of_the_brain_s_neurons_are_located_in_the,
title = {Claim Verification: “Over 80\% of the brain's neurons are located in the cerebellum.” — Proved},
author = {{Proof Engine}},
year = {2026},
url = {https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/},
note = {Verdict: PROVED. Generated by proof-engine v0.10.0},
}
TY - DATA TI - Claim Verification: “Over 80% of the brain's neurons are located in the cerebellum.” — Proved AU - Proof Engine PY - 2026 UR - https://proofengine.info/proofs/over-80-of-the-brain-s-neurons-are-located-in-the/ N1 - Verdict: PROVED. Generated by proof-engine v0.10.0 ER -
View proof source
This is the proof.py that produced the verdict above. Every fact traces to code below. (This proof has not yet been minted to Zenodo; the source here is the working copy from this repository.)
"""
Proof: Over 80% of the brain's neurons are located in the cerebellum.
Generated: 2026-03-27
"""
import json
from datetime import date
import re
import os
import sys
PROOF_ENGINE_ROOT = os.environ.get("PROOF_ENGINE_ROOT")
if not PROOF_ENGINE_ROOT:
_d = os.path.dirname(os.path.abspath(__file__))
while _d != os.path.dirname(_d):
if os.path.isdir(os.path.join(_d, "proof-engine", "skills", "proof-engine", "scripts")):
PROOF_ENGINE_ROOT = os.path.join(_d, "proof-engine", "skills", "proof-engine")
break
_d = os.path.dirname(_d)
if not PROOF_ENGINE_ROOT:
raise RuntimeError("PROOF_ENGINE_ROOT not set and skill dir not found via walk-up from proof.py")
sys.path.insert(0, PROOF_ENGINE_ROOT)
from scripts.smart_extract import normalize_unicode, verify_extraction
from scripts.verify_citations import verify_all_citations, build_citation_detail, verify_data_values
from scripts.computations import compare, explain_calc, cross_check
# 1. CLAIM INTERPRETATION (Rule 4)
CLAIM_NATURAL = "Over 80% of the brain's neurons are located in the cerebellum."
CLAIM_FORMAL = {
"subject": "human cerebellum",
"property": "percentage of total brain neurons located in the cerebellum",
"operator": ">",
"operator_note": (
"'Over 80%' is interpreted as strictly greater than 80.0%. "
"If the cerebellum held exactly 80.0% of neurons the claim would be FALSE. "
"'Brain' means the entire brain (cerebrum + cerebellum + brainstem) excluding "
"the spinal cord — the standard neuroanatomical usage in all cited sources. "
"The more conservative strict-greater-than reading is used; >= would make the "
"claim easier to prove."
),
"threshold": 80.0,
}
# 2. FACT REGISTRY
FACT_REGISTRY = {
"B1": {
"key": "source_a_total",
"label": "Total human brain neuron count — Herculano-Houzel 2009 (PMC2776484)"
},
"B2": {
"key": "source_a_cerebellum",
"label": "Cerebellum neuron count — Herculano-Houzel 2009 (PMC2776484)"
},
"B3": {
"key": "source_b",
"label": "Independent statement: cerebellum ~80% of brain neurons — von Bartheld et al. 2016 review (PMC5063692)"
},
"B4": {
"key": "source_c",
"label": "Cross-species comparison: 80% in human — Herculano-Houzel et al. 2010 Frontiers Neuroanatomy"
},
"A1": {
"label": "Computed cerebellum neuron %: (69 billion / 86 billion) × 100",
"method": None,
"result": None
},
}
# 3. EMPIRICAL FACTS (Rule 2)
empirical_facts = {
"source_a_total": {
"quote": "the adult male human brain, at an average of 1.5 kg, has 86 billion neurons and 85 billion non-neuronal cells",
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2776484/",
"source_name": "Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31. PMC2776484",
"data_values": {
"total_neurons": "86 billion neurons",
},
},
"source_a_cerebellum": {
"quote": "the human cerebellum, at 154 g and 69 billion neurons, matches or even slightly exceeds the expected",
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2776484/",
"source_name": "Herculano-Houzel S (2009) The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci 3:31. PMC2776484",
"data_values": {
"cerebellum_neurons": "69 billion neurons",
},
},
"source_b": {
"quote": "the cerebellum (which contains about 80% of all neurons in the human brain; Azevedo et al. (2009))",
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC5063692/",
"source_name": "von Bartheld CS, Bahney J, Herculano-Houzel S (2016) The search for true numbers of neurons and glial cells in the human brain. J Comp Neurol 524(18):3865-3895. PMC5063692",
},
"source_c": {
"quote": "the cerebellum holds 60% of all brain neurons in the mouse, small shrews, and marmoset; 70% in the rat, guinea pig and macaque; and 80% in the agouti, galago, and human",
"url": "https://www.frontiersin.org/journals/neuroanatomy/articles/10.3389/fnana.2010.00012/full",
"source_name": "Herculano-Houzel S, Catania K, Manger PR, Kaas JH (2010) Coordinated scaling of cortical and cerebellar numbers of neurons. Front Neuroanat 4:12",
},
}
# 4. CITATION VERIFICATION (Rule 2)
print("=== Verifying citations ===")
citation_results = verify_all_citations(empirical_facts, wayback_fallback=True)
# 5. DATA VALUE VERIFICATION
print("\n=== Verifying data values ===")
dv_total = verify_data_values(
empirical_facts["source_a_total"]["url"],
empirical_facts["source_a_total"]["data_values"],
"B1",
)
dv_cerebellum = verify_data_values(
empirical_facts["source_a_cerebellum"]["url"],
empirical_facts["source_a_cerebellum"]["data_values"],
"B2",
)
print(f"B1 data_values verification: {dv_total}")
print(f"B2 data_values verification: {dv_cerebellum}")
# Note per gotchas: if verify_data_values fails (JS-rendered page), the computation
# still proceeds using the quotes from the peer-reviewed paper, with a note that
# data value verification was inconclusive for this source.
b1_total_verified = dv_total.get("total_neurons", {}).get("found", False)
b2_cerebellum_verified = dv_cerebellum.get("cerebellum_neurons", {}).get("found", False)
# 6. VALUE EXTRACTION (Rule 1) — parse from quotes, never hand-type
def extract_billions_from_quote(quote, fact_id):
"""Extract 'N billion neurons' pattern and return count as float (absolute, not billions).
verify_extraction confirms the raw integer (N) appears in the quote string.
"""
normalized = normalize_unicode(quote)
m = re.search(r'(\d+) billion neurons', normalized)
if not m:
raise ValueError(
f"Could not parse 'N billion neurons' from {fact_id} quote: {quote!r}"
)
raw_int = int(m.group(1))
verify_extraction(raw_int, quote, fact_id)
return float(raw_int) * 1e9
total_neurons = extract_billions_from_quote(
empirical_facts["source_a_total"]["quote"], "B1"
)
cerebellum_neurons = extract_billions_from_quote(
empirical_facts["source_a_cerebellum"]["quote"], "B2"
)
print(f"\nExtracted total brain neurons: {total_neurons / 1e9:.0f} billion")
print(f"Extracted cerebellum neurons: {cerebellum_neurons / 1e9:.0f} billion")
# 7. COMPUTATION (Rule 7)
print("\n=== Computation ===")
pct = explain_calc(
"cerebellum_neurons / total_neurons * 100",
locals(),
label="Cerebellum % of total brain neurons"
)
FACT_REGISTRY["A1"]["method"] = "cerebellum_neurons / total_neurons * 100"
FACT_REGISTRY["A1"]["result"] = round(pct, 4)
# 8. CLAIM EVALUATION
print("\n=== Claim Evaluation ===")
claim_holds = compare(pct, ">", CLAIM_FORMAL["threshold"],
label="SC1: cerebellum neuron % > 80%")
# 9. CROSS-CHECK (Rule 6)
# Source B (PMC5063692) independently states "about 80%" — extract the percentage
print("\n=== Cross-check ===")
def extract_about_pct(quote, fact_id):
"""Extract 'about N%' pattern from quote."""
normalized = normalize_unicode(quote)
m = re.search(r'about (\d+)%', normalized)
if not m:
raise ValueError(f"Could not parse 'about N%' from {fact_id} quote: {quote!r}")
val = float(m.group(1))
verify_extraction(int(val), quote, fact_id)
return val
stated_pct_b3 = extract_about_pct(empirical_facts["source_b"]["quote"], "B3")
# Cross-check: computed value vs independently stated percentage
# Tolerance=2.0pp since source_b says "about 80%" (rounded figure)
cc_b3 = cross_check(
pct, stated_pct_b3,
tolerance=2.0, mode="absolute",
label="Computed 80.23% vs B3 stated ~80% (von Bartheld 2016)"
)
# Source C (Frontiers 2010) states "80% in human" — also consistent
def extract_human_pct(quote, fact_id):
"""Extract 'N% in the ... human' pattern."""
normalized = normalize_unicode(quote)
m = re.search(r'and (\d+)% in the agouti', normalized)
if not m:
raise ValueError(f"Could not parse human pct from {fact_id}: {quote!r}")
val = float(m.group(1))
verify_extraction(int(val), quote, fact_id)
return val
stated_pct_b4 = extract_human_pct(empirical_facts["source_c"]["quote"], "B4")
cc_b4 = cross_check(
pct, stated_pct_b4,
tolerance=2.0, mode="absolute",
label="Computed 80.23% vs B4 stated 80% (Herculano-Houzel 2010)"
)
# 10. ADVERSARIAL CHECKS (Rule 5)
adversarial_checks = [
{
"question": "Does any peer-reviewed source dispute that the cerebellum holds ~80% of brain neurons?",
"verification_performed": (
"Searched: 'cerebellum percentage brain neurons 80 percent counter-evidence dispute'. "
"Found brainfacts.org (2020) states 'more than half of its neurons' — a lower estimate. "
"Also found PMC5063692 Table 4 lists Andrade-Moraes et al. 2013 giving 54×10⁹ "
"cerebellum neurons vs Azevedo's 69×10⁹ — a 22% lower count. Using 54B cerebellum "
"of an assumed 86B total gives 62.8%, well below 80%. "
"All sources cite Azevedo et al. 2009 as the primary/gold-standard count. "
"Multiple peer-reviewed reviews (PMC5063692, PMC2776484, Frontiers 2010) "
"independently confirm the ~80% figure citing Azevedo 2009."
),
"finding": (
"The Andrade-Moraes 2013 estimate of 54B cerebellar neurons is a genuine "
"methodological alternative that would place the cerebellum well below 80% "
"of total neurons. However, Azevedo et al. 2009 using the isotropic fractionation "
"method is the current gold standard and is cited universally in reviews. "
"brainfacts.org is a popular-science source, not peer-reviewed. "
"No peer-reviewed paper argues the cerebellum holds ≤80% using the Azevedo methodology."
),
"breaks_proof": False,
},
{
"question": "If 'brain' included the spinal cord, would the percentage fall below 80%?",
"verification_performed": (
"Searched: 'human spinal cord neuron count'. "
"Herculano-Houzel et al. estimate the human spinal cord contains ~1 billion neurons. "
"Adding 1B to the 86B total: 69 / 87 = 79.3%."
),
"finding": (
"Including the spinal cord drops the cerebellum fraction to ~79.3%, below 80%. "
"However, 'brain' in neuroanatomy excludes the spinal cord by definition, "
"and all cited sources explicitly use 'brain' to mean the organ inside the skull. "
"The claim is TRUE under the standard definition."
),
"breaks_proof": False,
},
{
"question": "Is the margin of 0.23 percentage points (80.23% vs 80% threshold) within measurement error?",
"verification_performed": (
"Azevedo et al. 2009 report total brain neurons as 86.1 ± 8.1 billion and "
"cerebellum neurons as 69.03 ± 6.65 billion (standard deviations). "
"The ratio 69.03/86.1 = 80.2%. The standard deviation on the ratio is substantial. "
"Using the lower bound: (69.03-6.65)/(86.1+8.1) = 62.38/94.2 = 66.2%; "
"upper bound: (69.03+6.65)/(86.1-8.1) = 75.68/78.0 = 97.0%. "
"The measurement uncertainty spans a very wide range."
),
"finding": (
"The thin margin (0.23 pp) is within the measurement uncertainty of the underlying study. "
"The claim that it is OVER 80% (strictly) rests on the point estimate alone. "
"The scientific literature rounds to 'about 80%' — consistent with the claim "
"but not confirming the strictly-greater-than interpretation with high confidence. "
"This is noted as a genuine limitation but does not disprove the claim outright."
),
"breaks_proof": False,
},
{
"question": "Could 'over 80%' linguistically require 81%+?",
"verification_performed": "Linguistic analysis of 'over 80%'.",
"finding": (
"'Over 80%' in standard English means > 80.0%, not ≥ 81%. "
"80.23% satisfies > 80.0% by definition. This reading is used consistently "
"in statistical and scientific writing."
),
"breaks_proof": False,
},
]
# 11. VERDICT AND STRUCTURED OUTPUT
if __name__ == "__main__":
any_unverified = any(
cr["status"] != "verified" for cr in citation_results.values()
)
if claim_holds and not any_unverified:
verdict = "PROVED"
elif claim_holds and any_unverified:
verdict = "PROVED (with unverified citations)"
elif not claim_holds and not any_unverified:
verdict = "DISPROVED"
elif not claim_holds and any_unverified:
verdict = "DISPROVED (with unverified citations)"
else:
verdict = "UNDETERMINED"
FACT_REGISTRY["A1"]["method"] = "cerebellum_neurons / total_neurons * 100"
FACT_REGISTRY["A1"]["result"] = str(round(pct, 4))
citation_detail = build_citation_detail(FACT_REGISTRY, citation_results, empirical_facts)
extractions = {
"B1": {
"value": f"{total_neurons / 1e9:.0f} billion ({int(total_neurons):,})",
"value_in_quote": True,
"quote_snippet": empirical_facts["source_a_total"]["quote"][:80],
},
"B2": {
"value": f"{cerebellum_neurons / 1e9:.0f} billion ({int(cerebellum_neurons):,})",
"value_in_quote": True,
"quote_snippet": empirical_facts["source_a_cerebellum"]["quote"][:80],
},
"B3": {
"value": f"{stated_pct_b3:.0f}%",
"value_in_quote": True,
"quote_snippet": empirical_facts["source_b"]["quote"][:80],
},
"B4": {
"value": f"{stated_pct_b4:.0f}%",
"value_in_quote": True,
"quote_snippet": empirical_facts["source_c"]["quote"][:80],
},
}
summary = {
"fact_registry": {
fid: {k: v for k, v in info.items()}
for fid, info in FACT_REGISTRY.items()
},
"claim_formal": CLAIM_FORMAL,
"claim_natural": CLAIM_NATURAL,
"citations": citation_detail,
"extractions": extractions,
"cross_checks": [
{
"description": "Computed 80.23% vs B3 stated ~80% (von Bartheld 2016 review)",
"values_compared": [str(round(pct, 4)), str(stated_pct_b3)],
"tolerance": 2.0,
"mode": "absolute",
"agreement": cc_b3,
},
{
"description": "Computed 80.23% vs B4 stated 80% (Herculano-Houzel 2010)",
"values_compared": [str(round(pct, 4)), str(stated_pct_b4)],
"tolerance": 2.0,
"mode": "absolute",
"agreement": cc_b4,
},
],
"adversarial_checks": adversarial_checks,
"verdict": verdict,
"key_results": {
"cerebellum_neurons_billions": cerebellum_neurons / 1e9,
"total_neurons_billions": total_neurons / 1e9,
"cerebellum_pct": round(pct, 4),
"threshold": CLAIM_FORMAL["threshold"],
"operator": CLAIM_FORMAL["operator"],
"claim_holds": claim_holds,
"data_value_verification": {
"B1_total_found": b1_total_verified,
"B2_cerebellum_found": b2_cerebellum_verified,
},
},
"generator": {
"name": "proof-engine",
"version": "0.10.0",
"repo": "https://github.com/yaniv-golan/proof-engine",
"generated_at": date.today().isoformat(),
},
}
print("\n=== PROOF SUMMARY (JSON) ===")
print(json.dumps(summary, indent=2, default=str))
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