Pith Number

pith:O4XVK2CK

pith:2003:O4XVK2CK5ELCPW2MIBQZW4A6RU

not attested not anchored not stored refs pending

Homotopy Inner Products for Cyclic Operads

Riccardo Longoni, Thomas Tradler

arxiv:math/0312231 v1 · 2003-12-11 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O4XVK2CK5ELCPW2MIBQZW4A6RU}

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	2026-07-04T14:38:05.096793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

772f55684ae91627db4c40619b701e8d2b6c50d05130359db82816305663e8a9

Aliases

arxiv: math/0312231 · arxiv_version: math/0312231v1 · doi: 10.48550/arxiv.math/0312231 · pith_short_12: O4XVK2CK5ELC · pith_short_16: O4XVK2CK5ELCPW2M · pith_short_8: O4XVK2CK

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/O4XVK2CK5ELCPW2MIBQZW4A6RU \
  | 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: 772f55684ae91627db4c40619b701e8d2b6c50d05130359db82816305663e8a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfed68dac462c8566b038aca74874b0beda01693ba4da3bca7a6dba083ac867f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2003-12-11T10:04:12Z",
    "title_canon_sha256": "22663983502e17eefc821fc160cbaecefd855c0f0ff16e7b3a7e77bb10535e5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312231",
    "kind": "arxiv",
    "version": 1
  }
}