Pith Number

pith:TCNPMD7I

pith:2004:TCNPMD7IA5O6WSHBIL7D6SMRFN

not attested not anchored not stored refs pending

Free monoid in monoidal abelian categories

Bruno Vallette

arxiv:math/0411543 v2 · 2004-11-24 · math.CT · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TCNPMD7IA5O6WSHBIL7D6SMRFN}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-05-18T04:25:26.345526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

989af60fe8075deb48e142fe3f49912b6f800e02db483da90990d04f4ff36c2e

Aliases

arxiv: math/0411543 · arxiv_version: math/0411543v2 · doi: 10.48550/arxiv.math/0411543 · pith_short_12: TCNPMD7IA5O6 · pith_short_16: TCNPMD7IA5O6WSHB · pith_short_8: TCNPMD7I

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/TCNPMD7IA5O6WSHBIL7D6SMRFN \
  | 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: 989af60fe8075deb48e142fe3f49912b6f800e02db483da90990d04f4ff36c2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c16e80b6f42e899381e83c4f0ac3fc370e84565b4ae236c320540445df5b183",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CT",
    "submitted_at": "2004-11-24T10:28:18Z",
    "title_canon_sha256": "e73477bc7b33c6b818b34ed77d0b1362c8d7c42c46210cf51c3da1c14b894937"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411543",
    "kind": "arxiv",
    "version": 2
  }
}