Pith Number

pith:SPA4WC23

pith:2016:SPA4WC23553YPDIMHWJ5Z5DWNJ

not attested not anchored not stored refs pending

A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature

Richard C. Kraaij

arxiv:1609.09637 v1 · 2016-09-30 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SPA4WC23553YPDIMHWJ5Z5DWNJ}

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	2026-05-18T01:03:35.479610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93c1cb0b5bef77878d0c3d93dcf4766a567f2c7fe8af650c8fbeb73ec1d284f5

Aliases

arxiv: 1609.09637 · arxiv_version: 1609.09637v1 · doi: 10.48550/arxiv.1609.09637 · pith_short_12: SPA4WC23553Y · pith_short_16: SPA4WC23553YPDIM · pith_short_8: SPA4WC23

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/SPA4WC23553YPDIMHWJ5Z5DWNJ \
  | 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: 93c1cb0b5bef77878d0c3d93dcf4766a567f2c7fe8af650c8fbeb73ec1d284f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "612f2b949c299c378711b2272b0097a2d76c1ccb533329138b719e3e6bcb2e7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-30T08:54:09Z",
    "title_canon_sha256": "6b45faf354d193e208603712ba0c62ceb36bcc6a0f24f41ed3eaba22b3c27ff9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09637",
    "kind": "arxiv",
    "version": 1
  }
}