Pith Number

pith:Z6ZB3UJW

pith:2005:Z6ZB3UJWMDGVYC6SG6BKCMZO36

not attested not anchored not stored refs pending

Calculus of the first non-trivial 1-cocycle of the space of long knots

Victor Tourtchine

arxiv:math/0502518 v2 · 2005-02-24 · 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{Z6ZB3UJWMDGVYC6SG6BKCMZO36}

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

A Fox-Neuwirth Basis for the Sinha Spectral Sequence

Receipt and verification

First computed	2026-07-04T14:39:44.868053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfb21dd13660cd5c0bd23782a1332edfab77a10c54c2857d3247153d0bc23154

Aliases

arxiv: math/0502518 · arxiv_version: math/0502518v2 · doi: 10.48550/arxiv.math/0502518 · pith_short_12: Z6ZB3UJWMDGV · pith_short_16: Z6ZB3UJWMDGVYC6S · pith_short_8: Z6ZB3UJW

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/Z6ZB3UJWMDGVYC6SG6BKCMZO36 \
  | 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: cfb21dd13660cd5c0bd23782a1332edfab77a10c54c2857d3247153d0bc23154

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55249831bcfa89b7df78fc157f9ba37291b0680682c71561db465fb49642d347",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2005-02-24T16:05:55Z",
    "title_canon_sha256": "2f0e3a6bd72e3c9a929656cefc788b070c4705eef24670fbe1b7db973a994f55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502518",
    "kind": "arxiv",
    "version": 2
  }
}