Pith Number

pith:TINROHED

pith:2010:TINROHEDBU6PF4ZRNUC3RL4EXM

not attested not anchored not stored refs pending

Free products of sofic groups with amalgamation over monotileably amenable groups

Benoit Collins, Ken Dykema

arxiv:1003.1675 v4 · 2010-03-08 · math.GR · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TINROHEDBU6PF4ZRNUC3RL4EXM}

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	2026-05-18T04:02:25.365792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a1b171c830d3cf2f3316d05b8af84bb133870b86cc00c5554cd1abab8c33e6a

Aliases

arxiv: 1003.1675 · arxiv_version: 1003.1675v4 · doi: 10.48550/arxiv.1003.1675 · pith_short_12: TINROHEDBU6P · pith_short_16: TINROHEDBU6PF4ZR · pith_short_8: TINROHED

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/TINROHEDBU6PF4ZRNUC3RL4EXM \
  | 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: 9a1b171c830d3cf2f3316d05b8af84bb133870b86cc00c5554cd1abab8c33e6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cea3b467b6f92a3b40c5aad7382a9a06ffb1805f08f070fd633f5027675057b",
    "cross_cats_sorted": [
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-03-08T17:05:44Z",
    "title_canon_sha256": "81c26cfd4d612ce97be87a3420afad8142be172c6e3768b058c840ebfd50dae5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1675",
    "kind": "arxiv",
    "version": 4
  }
}