Pith Number

pith:QQ4TUBFW

pith:2004:QQ4TUBFWZZQEV72GE6QE65SFKJ

not attested not anchored not stored refs pending

Morita classes in the homology of automorphism groups of free groups

James Conant, Karen Vogtmann

arxiv:math/0406389 v2 · 2004-06-19 · math.QA · 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{QQ4TUBFWZZQEV72GE6QE65SFKJ}

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	2026-05-18T02:38:00.053929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84393a04b6ce604aff4627a04f76455261b1f8d2995c017a906f98f674e5f51e

Aliases

arxiv: math/0406389 · arxiv_version: math/0406389v2 · doi: 10.48550/arxiv.math/0406389 · pith_short_12: QQ4TUBFWZZQE · pith_short_16: QQ4TUBFWZZQEV72G · pith_short_8: QQ4TUBFW

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/QQ4TUBFWZZQEV72GE6QE65SFKJ \
  | 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: 84393a04b6ce604aff4627a04f76455261b1f8d2995c017a906f98f674e5f51e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a95efa42e360ee15f47c5d7e78453d922df2a4ae0ddb17a2ee9cbb19173ce0d3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2004-06-19T21:16:36Z",
    "title_canon_sha256": "f5a021f0787828f1272ad9fc4272f5a196cef75ff3f8b4215e4ec0cf2dae3416"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406389",
    "kind": "arxiv",
    "version": 2
  }
}