Pith Number

pith:AFP37YLU

pith:2012:AFP37YLU5L4DSJHJTI5ZGYKHT7

not attested not anchored not stored refs pending

Invariants of closed braids via counting surfaces

Michael Brandenbursky

arxiv:1209.1308 v3 · 2012-09-06 · 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{AFP37YLU5L4DSJHJTI5ZGYKHT7}

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	2026-05-18T02:20:50.441968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2

Aliases

arxiv: 1209.1308 · arxiv_version: 1209.1308v3 · doi: 10.48550/arxiv.1209.1308 · pith_short_12: AFP37YLU5L4D · pith_short_16: AFP37YLU5L4DSJHJ · pith_short_8: AFP37YLU

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/AFP37YLU5L4DSJHJTI5ZGYKHT7 \
  | 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: 015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a66948b4c9f641cb07449170bb0ebcdc6be689add04d07a1ba2ae3a1a35040a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-06T15:01:40Z",
    "title_canon_sha256": "576611378909531e76bf4418653997cb28a4a3c1192948a51a0f6e3862e146a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1308",
    "kind": "arxiv",
    "version": 3
  }
}