Pith Number

pith:BRMZA5ZZ

pith:2010:BRMZA5ZZVRPV3ASHP7EMEFL2UW

not attested not anchored not stored refs pending

Polynomial invariants of pseudo-Anosov maps

Joan Birman, Keiko Kawamuro, Peter Brinkmann

arxiv:1001.5094 v7 · 2010-01-28 · 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{BRMZA5ZZVRPV3ASHP7EMEFL2UW}

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	2026-05-18T03:57:37.495308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c59907739ac5f5d82477fc8c2157aa599edb3828452d9bee5d1a30b844b117a

Aliases

arxiv: 1001.5094 · arxiv_version: 1001.5094v7 · doi: 10.48550/arxiv.1001.5094 · pith_short_12: BRMZA5ZZVRPV · pith_short_16: BRMZA5ZZVRPV3ASH · pith_short_8: BRMZA5ZZ

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/BRMZA5ZZVRPV3ASHP7EMEFL2UW \
  | 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: 0c59907739ac5f5d82477fc8c2157aa599edb3828452d9bee5d1a30b844b117a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17dfc34571f4c05425f9b8b168a04ee865882fbc7fe3de903a1a84f26a2249dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-01-28T03:36:07Z",
    "title_canon_sha256": "49ce0d69501d10d396a4a7cc510837ee80f1c4fa0be38e4a5cf45d35144719f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.5094",
    "kind": "arxiv",
    "version": 7
  }
}