Pith Number

pith:4EZWTEZY

pith:2017:4EZWTEZYMDVT2JCAAFTINABGQQ

not attested not anchored not stored refs pending

Product and coproduct in string topology

Nancy Hingston, Nathalie Wahl

arxiv:1709.06839 v4 · 2017-09-20 · math.AT · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4EZWTEZYMDVT2JCAAFTINABGQQ}

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.

Cited by

1 paper in Pith

Graded Frobenius Algebras

Receipt and verification

First computed	2026-07-05T03:52:09.900480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e13369933860eb3d24400166868026842f6ce5491c320bc0b820c4c92ac2d49e

Aliases

arxiv: 1709.06839 · arxiv_version: 1709.06839v4 · doi: 10.48550/arxiv.1709.06839 · pith_short_12: 4EZWTEZYMDVT · pith_short_16: 4EZWTEZYMDVT2JCA · pith_short_8: 4EZWTEZY

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/4EZWTEZYMDVT2JCAAFTINABGQQ \
  | 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: e13369933860eb3d24400166868026842f6ce5491c320bc0b820c4c92ac2d49e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85e6a843155c21a79712154ed3ed10fdce185d3d7d1b936ad758ff9209d6b91a",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2017-09-20T12:52:47Z",
    "title_canon_sha256": "10025cf7af5cec3f9b3c6c2969dbc94c59bef6819832032019551045154c92a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06839",
    "kind": "arxiv",
    "version": 4
  }
}