Pith Number

pith:56VU242C

pith:2005:56VU242CF5YCVTGG7GQLFYMIVW

not attested not anchored not stored refs pending

On 2-Dimensional Homotopy Invariants of Complements of Knotted Surfaces

Jo\~ao Faria Martins

arxiv:math/0507239 v3 · 2005-07-12 · math.GT · 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{56VU242CF5YCVTGG7GQLFYMIVW}

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	2026-05-18T01:08:50.984349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efab4d73422f702accc6f9a0b2e188ad96d397c687419d163cc69f76eb8e99e2

Aliases

arxiv: math/0507239 · arxiv_version: math/0507239v3 · doi: 10.48550/arxiv.math/0507239 · pith_short_12: 56VU242CF5YC · pith_short_16: 56VU242CF5YCVTGG · pith_short_8: 56VU242C

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/56VU242CF5YCVTGG7GQLFYMIVW \
  | 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: efab4d73422f702accc6f9a0b2e188ad96d397c687419d163cc69f76eb8e99e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9546edbab72cf001b423427fea7698e8eddb60fbf06a90bd989d11f8dc1d7785",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-07-12T17:34:40Z",
    "title_canon_sha256": "1686119e178697ab5a10a7073f425c9e28ee3493317ddb593c0db99bcb92d80e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507239",
    "kind": "arxiv",
    "version": 3
  }
}