Pith Number

pith:M5PH5PSS

pith:2015:M5PH5PSS4X2FJSNA4Q6EC3QUQK

not attested not anchored not stored refs pending

A note on nonabelian Freiman-Ruzsa

Sean Eberhard

arxiv:1511.06758 v2 · 2015-11-20 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M5PH5PSS4X2FJSNA4Q6EC3QUQK}

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	2026-05-18T01:26:09.094578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

675e7ebe52e5f454c9a0e43c416e1482a3e7e1a77d119d7686498bcfeab7e1e0

Aliases

arxiv: 1511.06758 · arxiv_version: 1511.06758v2 · doi: 10.48550/arxiv.1511.06758 · pith_short_12: M5PH5PSS4X2F · pith_short_16: M5PH5PSS4X2FJSNA · pith_short_8: M5PH5PSS

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/M5PH5PSS4X2FJSNA4Q6EC3QUQK \
  | 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: 675e7ebe52e5f454c9a0e43c416e1482a3e7e1a77d119d7686498bcfeab7e1e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a1afc1c65a7a983744a0aebcd7d7d6d91d49d022bd12f209cca5dd602fc4cf3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-11-20T17:12:55Z",
    "title_canon_sha256": "e77aca94856197ed3f9fc8f5bb6bf0a14b6af0afa832c2dc94d186612df000fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06758",
    "kind": "arxiv",
    "version": 2
  }
}