Pith Number

pith:7XSJPXFA

pith:2022:7XSJPXFALJMMRFZWUHTFE7YTIQ

not attested not anchored not stored refs pending

The free factor complex and the dualizing module for the automorphism group of a free group

Andrew Putman, Jeremy Miller, Sam Nariman, Zachary Himes

arxiv:2203.03102 v3 · 2022-03-07 · math.AT · 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{7XSJPXFALJMMRFZWUHTFE7YTIQ}

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	2026-07-05T07:14:49.802276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde497dca05a58c89736a1e6527f13443aee64b366b335403717abadf49397d3

Aliases

arxiv: 2203.03102 · arxiv_version: 2203.03102v3 · doi: 10.48550/arxiv.2203.03102 · pith_short_12: 7XSJPXFALJMM · pith_short_16: 7XSJPXFALJMMRFZW · pith_short_8: 7XSJPXFA

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/7XSJPXFALJMMRFZWUHTFE7YTIQ \
  | 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: fde497dca05a58c89736a1e6527f13443aee64b366b335403717abadf49397d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39e6cabdd064f250239538dc6537e5575e00f38e1e33cadb14f729f075d496cd",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2022-03-07T02:20:32Z",
    "title_canon_sha256": "8a1a353bd8fe59f8c56c7a6c3a91cb5ba19435c9ae7a273e345e46f5cb87bc8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.03102",
    "kind": "arxiv",
    "version": 3
  }
}