Pith Number

pith:B45JVGCQ

pith:2007:B45JVGCQ74327WLL7VHDM25CCF

not attested not anchored not stored refs pending

The rational homology of spaces of long knots in codimension >2

Ismar Volic, Pascal Lambrechts, Victor Tourtchine

arxiv:math/0703649 v1 · 2007-03-21 · math.AT · 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{B45JVGCQ74327WLL7VHDM25CCF}

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	2026-05-18T02:37:59.382095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f3a9a9850ff37afd96bfd4e366ba2117f41510736c06412f64448e0c585e740

Aliases

arxiv: math/0703649 · arxiv_version: math/0703649v1 · doi: 10.48550/arxiv.math/0703649 · pith_short_12: B45JVGCQ7432 · pith_short_16: B45JVGCQ74327WLL · pith_short_8: B45JVGCQ

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/B45JVGCQ74327WLL7VHDM25CCF \
  | 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: 0f3a9a9850ff37afd96bfd4e366ba2117f41510736c06412f64448e0c585e740

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aefcd2416e7742aeb7945d84bb0d208d6b84d84257a5b288e4d7dc46683f5d7d",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2007-03-21T20:14:07Z",
    "title_canon_sha256": "02ab7a3564f05d24eb9c3eca18fb499a745d63e191aa906850a7b872ec5f71ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703649",
    "kind": "arxiv",
    "version": 1
  }
}