Pith Number

pith:D5QI4GQP

pith:2017:D5QI4GQPOK356LGGTILIKC6XHL

not attested not anchored not stored refs pending

One dimensional weighted Ricci curvature and displacement convexity of entropies

Yohei Sakurai

arxiv:1706.08225 v3 · 2017-06-26 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D5QI4GQPOK356LGGTILIKC6XHL}

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	2026-07-05T01:10:10.052839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f608e1a0f72b7df2cc69a16850bd73adb6ff371ff851d1f5c095ff02cdc1f82

Aliases

arxiv: 1706.08225 · arxiv_version: 1706.08225v3 · doi: 10.48550/arxiv.1706.08225 · pith_short_12: D5QI4GQPOK35 · pith_short_16: D5QI4GQPOK356LGG · pith_short_8: D5QI4GQP

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/D5QI4GQPOK356LGGTILIKC6XHL \
  | 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: 1f608e1a0f72b7df2cc69a16850bd73adb6ff371ff851d1f5c095ff02cdc1f82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df5adea42f4aeeb5120fa2fd6daed2d921225835e8116941adc31346eece48f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-06-26T04:25:05Z",
    "title_canon_sha256": "1b1122e3622135a3d320d2496cfb55a6de36f418f5c08d0089ef51ba3a7e2bf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.08225",
    "kind": "arxiv",
    "version": 3
  }
}