Pith Number

pith:Q2TOA3OO

pith:2014:Q2TOA3OOLYVM5NUAFWZCAHNRAW

not attested not anchored not stored refs pending

Deciding reducibility of mapping classes is in $\textbf{NP}$

Mark C. Bell

arxiv:1403.2997 v3 · 2014-03-12 · 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{Q2TOA3OOLYVM5NUAFWZCAHNRAW}

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	2026-05-18T01:29:21.873926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86a6e06dce5e2aceb6802db2201db1059b78f87498fe3b4f0e83796f7234d798

Aliases

arxiv: 1403.2997 · arxiv_version: 1403.2997v3 · doi: 10.48550/arxiv.1403.2997 · pith_short_12: Q2TOA3OOLYVM · pith_short_16: Q2TOA3OOLYVM5NUA · pith_short_8: Q2TOA3OO

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/Q2TOA3OOLYVM5NUAFWZCAHNRAW \
  | 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: 86a6e06dce5e2aceb6802db2201db1059b78f87498fe3b4f0e83796f7234d798

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04ab274326565a1a1a05d000c22ee59f13fe7bb57cf0d9c232329b000269d9d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-03-12T16:05:55Z",
    "title_canon_sha256": "6065c0bb57957330e1e9b469a260f893f6ac618da27ac3c4823dee9bf2b93583"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.2997",
    "kind": "arxiv",
    "version": 3
  }
}