Pith Number

pith:7JGTHK5A

pith:2006:7JGTHK5ARFLXXA7XJXUUL75G6Q

not attested not anchored not stored refs pending

Erratum to: Homology stability for outer automorphism groups of free groups

Allen Hatcher, Karen Vogtmann, Nathalie Wahl

arxiv:math/0603577 v1 · 2006-03-24 · math.GR · 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{7JGTHK5ARFLXXA7XJXUUL75G6Q}

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	2026-05-18T02:41:31.883878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa4d33aba089577b83f74de945ffa6f435c6f7c5aa032c5349a615b7c8c9b36c

Aliases

arxiv: math/0603577 · arxiv_version: math/0603577v1 · doi: 10.48550/arxiv.math/0603577 · pith_short_12: 7JGTHK5ARFLX · pith_short_16: 7JGTHK5ARFLXXA7X · pith_short_8: 7JGTHK5A

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/7JGTHK5ARFLXXA7XJXUUL75G6Q \
  | 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: fa4d33aba089577b83f74de945ffa6f435c6f7c5aa032c5349a615b7c8c9b36c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5048d006a15210dc96f087e1477e77c672cc1550fd269ea9b685ab5e1bf6c11",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-03-24T15:19:24Z",
    "title_canon_sha256": "95fe2c1ca549c443e71514a31b0377f7a6a36268190d74cfac67716708f8c8ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603577",
    "kind": "arxiv",
    "version": 1
  }
}