Pith Number

pith:S6VUCCDW

pith:2026:S6VUCCDWPW3R7KBJXNIPBIHIDH

not attested not anchored not stored refs pending

Bennett's Conjecture in Lean 4: Counter-Models for the PSR-Reducibility of Spinoza's Propositions V and XIV

Yuki Nakamura

A four-element counter-model in Lean 4 satisfies Spinoza's axioms plus substantive PSR yet falsifies the full content of Proposition V.

arxiv:2605.02331 v2 · 2026-05-04 · cs.LO · math.LO

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\usepackage{pith}
\pithnumber{S6VUCCDWPW3R7KBJXNIPBIHIDH}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

A four-element counter-model satisfying both axiom sets while falsifying Proposition V's content establishes the irreducibility against this specific augmentation.

C2weakest assumption

The Lean encoding of Bennett's reading of Spinoza's stated axioms as a typeclass and Della Rocca's substantive PSR as an extension class faithfully captures the original philosophical commitments without introducing extraneous strength or weakness.

C3one line summary

Lean 4 counter-models confirm Spinoza's Proposition V cannot be derived from his axioms plus Della Rocca's substantive PSR, supporting Bennett's conjecture on the all-attributes ceiling.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:06:09.602999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97ab4108767db71fa829bb50f0a0e819f24d0daf4dce701efa46dbf9c8f5edcb

Aliases

arxiv: 2605.02331 · arxiv_version: 2605.02331v2 · doi: 10.48550/arxiv.2605.02331 · pith_short_12: S6VUCCDWPW3R · pith_short_16: S6VUCCDWPW3R7KBJ · pith_short_8: S6VUCCDW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/S6VUCCDWPW3R7KBJXNIPBIHIDH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 97ab4108767db71fa829bb50f0a0e819f24d0daf4dce701efa46dbf9c8f5edcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3626243dfdfcefb3c4fb7e0259aa01a7300950947fbd54092baa9fe37d1978c9",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-04T08:32:13Z",
    "title_canon_sha256": "3f7cb75dd7039b17f3101d088cdf15559620e5327fe720f5749cb765da255831"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02331",
    "kind": "arxiv",
    "version": 2
  }
}