Pith Number

pith:O36NO7XL

pith:2011:O36NO7XLDL7AFUYXMXTQKAFRKH

not attested not anchored not stored refs pending

A Birman exact sequence for Aut(F_n)

Andrew Putman, Matthew B. Day

arxiv:1104.2371 v3 · 2011-04-13 · math.GT · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O36NO7XLDL7AFUYXMXTQKAFRKH}

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	2026-07-05T01:08:08.316115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76fcd77eeb1afe02d31765e70500b151ce6c1fc87baa2f08880b0c34aef718a2

Aliases

arxiv: 1104.2371 · arxiv_version: 1104.2371v3 · doi: 10.48550/arxiv.1104.2371 · pith_short_12: O36NO7XLDL7A · pith_short_16: O36NO7XLDL7AFUYX · pith_short_8: O36NO7XL

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/O36NO7XLDL7AFUYXMXTQKAFRKH \
  | 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: 76fcd77eeb1afe02d31765e70500b151ce6c1fc87baa2f08880b0c34aef718a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64f467c5659727c2b1b8d869af85889c0f16473c273df207be96312379215d05",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-04-13T04:06:59Z",
    "title_canon_sha256": "63cd1e2bffc168440f2672905078d8d8d7530ab91f1ab80821d446e638389b7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2371",
    "kind": "arxiv",
    "version": 3
  }
}