Pith Number

pith:MVTN7IMD

pith:2007:MVTN7IMDK5IXPJ23ONRIY3F3GU

not attested not anchored not stored refs pending

Non-trivalent graph cocycle and cohomology of the long knot space

Keiichi Sakai

arxiv:0711.4419 v3 · 2007-11-28 · math.GT · 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{MVTN7IMDK5IXPJ23ONRIY3F3GU}

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	2026-05-18T02:41:51.865101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6566dfa183575177a75b73628c6cbb350250a3601afd550d9c919d2c6b135f4d

Aliases

arxiv: 0711.4419 · arxiv_version: 0711.4419v3 · doi: 10.48550/arxiv.0711.4419 · pith_short_12: MVTN7IMDK5IX · pith_short_16: MVTN7IMDK5IXPJ23 · pith_short_8: MVTN7IMD

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/MVTN7IMDK5IXPJ23ONRIY3F3GU \
  | 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: 6566dfa183575177a75b73628c6cbb350250a3601afd550d9c919d2c6b135f4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b746199beea0dd09314780f2f218701106a45b18072d983062bd28abf7ced3f3",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2007-11-28T10:03:24Z",
    "title_canon_sha256": "2dc0d0d6ba689b3b295dc3e89bfd0a8e1b172ec20cf30da4e4824be3dfe07fa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.4419",
    "kind": "arxiv",
    "version": 3
  }
}