Pith Number

pith:O3Y6JSZM

pith:2019:O3Y6JSZMC3FS3FJJVDWFYGX5O2

not attested not anchored not stored refs pending

Serre's Property (FA) for automorphism groups of free products

Naomi Andrew

arxiv:1907.07022 v1 · 2019-07-16 · 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{O3Y6JSZMC3FS3FJJVDWFYGX5O2}

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	2026-05-17T23:40:28.331195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f1e4cb2c16cb2d9529a8ec5c1afd76b9b2f1664084322a379fb71776753f9b

Aliases

arxiv: 1907.07022 · arxiv_version: 1907.07022v1 · doi: 10.48550/arxiv.1907.07022 · pith_short_12: O3Y6JSZMC3FS · pith_short_16: O3Y6JSZMC3FS3FJJ · pith_short_8: O3Y6JSZM

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/O3Y6JSZMC3FS3FJJVDWFYGX5O2 \
  | 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: 76f1e4cb2c16cb2d9529a8ec5c1afd76b9b2f1664084322a379fb71776753f9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fffb1e910bac4f664b51e293550e08337d7be5871a7424a30c4334b9b5cafc8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-07-16T14:14:11Z",
    "title_canon_sha256": "955f58683010efc1d986915ffdafcc429d638040b2091f918db2b0af7ac1ef05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.07022",
    "kind": "arxiv",
    "version": 1
  }
}