Pith Number

pith:7FKFZCJX

pith:2013:7FKFZCJXEPUS5MBQ43T5RNGTLH

not attested not anchored not stored refs pending

An elementary proof for that all unoriented spanning surfaces of a link are related by attaching/deleting tubes and M\"{o}bius bands

Akira Yasuhara

arxiv:1307.5388 v1 · 2013-07-20 · 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{7FKFZCJXEPUS5MBQ43T5RNGTLH}

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	2026-05-18T03:17:55.945702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9545c893723e92eb030e6e7d8b4d359cecba1f641104e4433b6fe7fcd90f4f0

Aliases

arxiv: 1307.5388 · arxiv_version: 1307.5388v1 · doi: 10.48550/arxiv.1307.5388 · pith_short_12: 7FKFZCJXEPUS · pith_short_16: 7FKFZCJXEPUS5MBQ · pith_short_8: 7FKFZCJX

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/7FKFZCJXEPUS5MBQ43T5RNGTLH \
  | 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: f9545c893723e92eb030e6e7d8b4d359cecba1f641104e4433b6fe7fcd90f4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f14b5400c0b7e342ef08e64aeecc89d2fba2ab2726be0e1558ecbff8ee0cda83",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-20T07:59:52Z",
    "title_canon_sha256": "8def6b86cbd5fab4fa007a420cd9482c3aac5810cb73cda4eac3e7a0ebc45475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5388",
    "kind": "arxiv",
    "version": 1
  }
}