Pith Number

pith:3KFM5OBQ

pith:2012:3KFM5OBQS6V6CBWONNR6MWWGJ2

not attested not anchored not stored refs pending

On virtual link invariants

Alexander Schrijver

arxiv:1211.3572 v2 · 2012-11-15 · math.QA · math.CO · 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{3KFM5OBQS6V6CBWONNR6MWWGJ2}

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	2026-05-18T03:40:25.099865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da8aceb83097abe106ce6b63e65ac64e8c24210d2d2c8dd6b4e9578bfbd5a16b

Aliases

arxiv: 1211.3572 · arxiv_version: 1211.3572v2 · doi: 10.48550/arxiv.1211.3572 · pith_short_12: 3KFM5OBQS6V6 · pith_short_16: 3KFM5OBQS6V6CBWO · pith_short_8: 3KFM5OBQ

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/3KFM5OBQS6V6CBWONNR6MWWGJ2 \
  | 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: da8aceb83097abe106ce6b63e65ac64e8c24210d2d2c8dd6b4e9578bfbd5a16b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c58b8ffc4f25f4171de8e912c6f1ca15d572d448c7594daa56fb9275fb28143c",
    "cross_cats_sorted": [
      "math.CO",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-11-15T10:58:18Z",
    "title_canon_sha256": "b3f6bcc69dcf2452bef34f413eaffb45b13d31241f98a47c39be029d85aeed4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3572",
    "kind": "arxiv",
    "version": 2
  }
}