Pith Number

pith:7FBG2QCZ

pith:2016:7FBG2QCZFQJ3D3BM7FYTCJARWJ

not attested not anchored not stored refs pending

Whitney towers and abelian invariants of knots

Jae Choon Cha, Kent E. Orr, Mark Powell

arxiv:1606.03608 v2 · 2016-06-11 · 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{7FBG2QCZFQJ3D3BM7FYTCJARWJ}

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	2026-05-17T23:52:44.682615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9426d40592c13b1ec2cf971312411b2539cca1dcff7bc41c27cc0e9090d2521

Aliases

arxiv: 1606.03608 · arxiv_version: 1606.03608v2 · doi: 10.48550/arxiv.1606.03608 · pith_short_12: 7FBG2QCZFQJ3 · pith_short_16: 7FBG2QCZFQJ3D3BM · pith_short_8: 7FBG2QCZ

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/7FBG2QCZFQJ3D3BM7FYTCJARWJ \
  | 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: f9426d40592c13b1ec2cf971312411b2539cca1dcff7bc41c27cc0e9090d2521

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a42332acc2188df8b660e84f0af52a693847e8602f540b631370e14104548a6d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-06-11T15:37:16Z",
    "title_canon_sha256": "19ccd5c11c8f63684799a6cc94fbe1525f6a71f95501f4c7c64c678ddf41ddd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03608",
    "kind": "arxiv",
    "version": 2
  }
}