Pith Number

pith:4O4TPXVF

pith:2005:4O4TPXVFTCM5LWNIANQN5BDGMO

not attested not anchored not stored refs pending

The homotopy invariance of the string topology loop product and string bracket

Dennis Sullivan, John Klein, Ralph L. Cohen

arxiv:math/0509667 v2 · 2005-09-28 · math.GT · 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{4O4TPXVFTCM5LWNIANQN5BDGMO}

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	2026-05-18T02:57:51.039614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3b937dea59899d5d9a80360de846663bb92376fc8eedaf45df01a80b6dba25a

Aliases

arxiv: math/0509667 · arxiv_version: math/0509667v2 · doi: 10.48550/arxiv.math/0509667 · pith_short_12: 4O4TPXVFTCM5 · pith_short_16: 4O4TPXVFTCM5LWNI · pith_short_8: 4O4TPXVF

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/4O4TPXVFTCM5LWNIANQN5BDGMO \
  | 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: e3b937dea59899d5d9a80360de846663bb92376fc8eedaf45df01a80b6dba25a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef7060c4bf5404846a4dc3fec4b33415285cdfca79eecabc967079192783452e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2005-09-28T17:06:23Z",
    "title_canon_sha256": "8443567c4d7a199a7cb2d68700ea09c14c988eb5ac444b8892b9605a03e9b887"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509667",
    "kind": "arxiv",
    "version": 2
  }
}