Pith Number

pith:VG4FLSRG

pith:2004:VG4FLSRGZFF2VPYMOZDOGWZL5K

not attested not anchored not stored refs pending

Brunnian local moves of knots and Vassiliev invariants

Akira Yasuhara

arxiv:math/0412489 v1 · 2004-12-24 · 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{VG4FLSRGZFF2VPYMOZDOGWZL5K}

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	2026-07-04T14:39:29.434200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9b855ca26c94baabf0c7646e35b2bea83313083e54fce5c70318b945b6f7a7a

Aliases

arxiv: math/0412489 · arxiv_version: math/0412489v1 · doi: 10.48550/arxiv.math/0412489 · pith_short_12: VG4FLSRGZFF2 · pith_short_16: VG4FLSRGZFF2VPYM · pith_short_8: VG4FLSRG

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/VG4FLSRGZFF2VPYMOZDOGWZL5K \
  | 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: a9b855ca26c94baabf0c7646e35b2bea83313083e54fce5c70318b945b6f7a7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0bdac431e6575b13eec6a1de64e8c5214092cbcf75d384e05b1de6e61abdebb",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-12-24T13:42:26Z",
    "title_canon_sha256": "297bd763f392ca26a31e0a482b6d73a5bebb80655e8e1c3e6659166697062a63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412489",
    "kind": "arxiv",
    "version": 1
  }
}