Pith Number

pith:YDVFLO7X

pith:2015:YDVFLO7XJBY2SLSWKI2LHTFROD

not attested not anchored not stored refs pending

Weak amenability is stable under graph products

Eric Reckwerdt

arxiv:1511.04645 v3 · 2015-11-15 · 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{YDVFLO7XJBY2SLSWKI2LHTFROD}

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	2026-05-18T00:41:28.254480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0ea55bbf74871a92e565234b3ccb170dbd06dd9250fa52317ca8cfadc6d5c32

Aliases

arxiv: 1511.04645 · arxiv_version: 1511.04645v3 · doi: 10.48550/arxiv.1511.04645 · pith_short_12: YDVFLO7XJBY2 · pith_short_16: YDVFLO7XJBY2SLSW · pith_short_8: YDVFLO7X

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/YDVFLO7XJBY2SLSWKI2LHTFROD \
  | 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: c0ea55bbf74871a92e565234b3ccb170dbd06dd9250fa52317ca8cfadc6d5c32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "040775cc53d0a92491bd0a052f9ee5aba657fee5f08c21d5ecb336a115f7090f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-11-15T02:33:19Z",
    "title_canon_sha256": "4a10d8628e0097ee219f1b0e773b7525090ceb708fbadc9ece677d1c06292a6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04645",
    "kind": "arxiv",
    "version": 3
  }
}