Pith Number

pith:6UKTYYHN

pith:2015:6UKTYYHNN3UDTHNCAQ7JMPQYJF

not attested not anchored not stored refs pending

Bridge trisections of knotted surfaces in $S^4$

Alexander Zupan, Jeffrey Meier

arxiv:1507.08370 v1 · 2015-07-30 · 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{6UKTYYHNN3UDTHNCAQ7JMPQYJF}

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	2026-05-18T00:38:23.645512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5153c60ed6ee8399da2043e963e184953048ba94330d52c1f8b3de8b9bf97b3

Aliases

arxiv: 1507.08370 · arxiv_version: 1507.08370v1 · doi: 10.48550/arxiv.1507.08370 · pith_short_12: 6UKTYYHNN3UD · pith_short_16: 6UKTYYHNN3UDTHNC · pith_short_8: 6UKTYYHN

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/6UKTYYHNN3UDTHNCAQ7JMPQYJF \
  | 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: f5153c60ed6ee8399da2043e963e184953048ba94330d52c1f8b3de8b9bf97b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d37db9bb7629d808a495a7b17233b9002c1a19232b61f59de953a6ba5cd9662",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-07-30T04:08:31Z",
    "title_canon_sha256": "1748d943a319549012f8eab88bb8d5bd24fbc83fde45a584dda85102a6b5327b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08370",
    "kind": "arxiv",
    "version": 1
  }
}