Pith Number

pith:ZKBXMUTF

pith:2015:ZKBXMUTFSPSHK5O6ITPHPUWFYX

not attested not anchored not stored refs pending

Thurston norm via Fox calculus

Kevin Schreve, Stefan Friedl, Stephan Tillmann

arxiv:1507.05660 v1 · 2015-07-20 · 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{ZKBXMUTFSPSHK5O6ITPHPUWFYX}

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	2026-05-18T00:21:00.340839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca8376526593e47575de44de77d2c5c5d81ed88305094dd08b8f629c0bb640f5

Aliases

arxiv: 1507.05660 · arxiv_version: 1507.05660v1 · doi: 10.48550/arxiv.1507.05660 · pith_short_12: ZKBXMUTFSPSH · pith_short_16: ZKBXMUTFSPSHK5O6 · pith_short_8: ZKBXMUTF

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/ZKBXMUTFSPSHK5O6ITPHPUWFYX \
  | 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: ca8376526593e47575de44de77d2c5c5d81ed88305094dd08b8f629c0bb640f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "789e936899ef141fb3884f4db6668485f733e778560b1afaedbda24d86803c02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-07-20T21:25:15Z",
    "title_canon_sha256": "e545f7bea609d5d87684a6611d16a94d6dba0cd88e2cd6b99d6c6e7bf0404cc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05660",
    "kind": "arxiv",
    "version": 1
  }
}