Pith Number

pith:6PQEFWMW

pith:2004:6PQEFWMWT5M65W3622HMZ7TOEG

not attested not anchored not stored refs pending

Stabilization for the automorphisms of free groups with boundaries

Allen Hatcher, Nathalie Wahl

arxiv:math/0406277 v2 · 2004-06-14 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PQEFWMWT5M65W3622HMZ7TOEG}

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	2026-05-18T02:38:00.060654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3e042d9969f59eedb7ed68eccfe6e21a137929ba5fa6d977a4063b24ef31351

Aliases

arxiv: math/0406277 · arxiv_version: math/0406277v2 · doi: 10.48550/arxiv.math/0406277 · pith_short_12: 6PQEFWMWT5M6 · pith_short_16: 6PQEFWMWT5M65W36 · pith_short_8: 6PQEFWMW

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/6PQEFWMWT5M65W3622HMZ7TOEG \
  | 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: f3e042d9969f59eedb7ed68eccfe6e21a137929ba5fa6d977a4063b24ef31351

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bec57f32997c9386eb8986a3246d0a0200c742c05a793d48698578a4e87cd899",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-06-14T17:23:22Z",
    "title_canon_sha256": "6c5d7adf24301b217d3ff1bdd53800207cb7bcb7ebe8d492b18ba70a0f5b29f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406277",
    "kind": "arxiv",
    "version": 2
  }
}