Pith Number

pith:B7AIX5NW

pith:2012:B7AIX5NWWO6ZVFOMM53QAOXOLR

not attested not anchored not stored refs pending

The Bubble Skein Element and Applications

Mustafa Hajij

arxiv:1212.2224 v4 · 2012-12-10 · math.GT · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B7AIX5NWWO6ZVFOMM53QAOXOLR}

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	2026-05-18T00:43:09.974487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fc08bf5b6b3bd9a95cc6777003aee5c5ba11651b7ddd3f52944cd0598dbf194

Aliases

arxiv: 1212.2224 · arxiv_version: 1212.2224v4 · doi: 10.48550/arxiv.1212.2224 · pith_short_12: B7AIX5NWWO6Z · pith_short_16: B7AIX5NWWO6ZVFOM · pith_short_8: B7AIX5NW

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/B7AIX5NWWO6ZVFOMM53QAOXOLR \
  | 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: 0fc08bf5b6b3bd9a95cc6777003aee5c5ba11651b7ddd3f52944cd0598dbf194

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7b86da17d44f3b6de64a06fc6729726bbd16a5b0b1878b16a69b0c013e563ee",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-10T21:29:03Z",
    "title_canon_sha256": "3e1985ff043bcf9901dcf404485f45f07675b2154b650cf98884fa62cf41034c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2224",
    "kind": "arxiv",
    "version": 4
  }
}