Pith Number

pith:BXZMUREK

pith:2003:BXZMUREKK5S7SBM5HUNE3QJEDX

not attested not anchored not stored refs pending

Simple Whitney towers, half-gropes and the Arf invariant of a knot

Rob Schneiderman

arxiv:math/0310304 v2 · 2003-10-20 · 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{BXZMUREKK5S7SBM5HUNE3QJEDX}

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	2026-05-18T04:02:01.295999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0df2ca448a5765f9059d3d1a4dc1241dfdf669fa20e393c3da8cca51a902f9ba

Aliases

arxiv: math/0310304 · arxiv_version: math/0310304v2 · doi: 10.48550/arxiv.math/0310304 · pith_short_12: BXZMUREKK5S7 · pith_short_16: BXZMUREKK5S7SBM5 · pith_short_8: BXZMUREK

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/BXZMUREKK5S7SBM5HUNE3QJEDX \
  | 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: 0df2ca448a5765f9059d3d1a4dc1241dfdf669fa20e393c3da8cca51a902f9ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abb9997cf87b1ea7ae5b0eb17e88a0914ae57545cf5fa070064f472e45c55cda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2003-10-20T01:34:24Z",
    "title_canon_sha256": "0dea345d84d8bae9e604b6f12ac5529f52298279520c7caa86ff5d1412c8b695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0310304",
    "kind": "arxiv",
    "version": 2
  }
}