Pith Number

pith:YYVML2IY

pith:2002:YYVML2IYOT3LKOWETGO6AJ2I4P

not attested not anchored not stored refs pending

The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

Vladimir Chernov (Tchernov)

arxiv:math/0209027 v2 · 2002-09-03 · 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{YYVML2IYOT3LKOWETGO6AJ2I4P}

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	2026-05-18T02:41:32.896271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c62ac5e91874f6b53ac4999de02748e3c18486f83da7cc99c47be0f835ae62ee

Aliases

arxiv: math/0209027 · arxiv_version: math/0209027v2 · doi: 10.48550/arxiv.math/0209027 · pith_short_12: YYVML2IYOT3L · pith_short_16: YYVML2IYOT3LKOWE · pith_short_8: YYVML2IY

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/YYVML2IYOT3LKOWETGO6AJ2I4P \
  | 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: c62ac5e91874f6b53ac4999de02748e3c18486f83da7cc99c47be0f835ae62ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb95ed78feebe466c2d859becdd60108dcf5190d34a0825bcd04f0b51ee83635",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-09-03T17:16:18Z",
    "title_canon_sha256": "81f2b9a50ac45c66bf31aefa87dda3680eea11850150a240ce1bd9fae611fca9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209027",
    "kind": "arxiv",
    "version": 2
  }
}