Pith Number

pith:WMJ4YB3R

pith:2011:WMJ4YB3RQYRXCQV3G5KRLL5SCQ

not attested not anchored not stored refs pending

Displacement convexity of generalized relative entropies.II

Asuka Takatsu, Shin-ichi Ohta

arxiv:1112.5554 v3 · 2011-12-23 · math.DG · math.AP · 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{WMJ4YB3RQYRXCQV3G5KRLL5SCQ}

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	2026-05-18T03:28:54.079737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b313cc077186237142bb375515afb2141940a179e9f80c58dcc91eaabf2926cf

Aliases

arxiv: 1112.5554 · arxiv_version: 1112.5554v3 · doi: 10.48550/arxiv.1112.5554 · pith_short_12: WMJ4YB3RQYRX · pith_short_16: WMJ4YB3RQYRXCQV3 · pith_short_8: WMJ4YB3R

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/WMJ4YB3RQYRXCQV3G5KRLL5SCQ \
  | 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: b313cc077186237142bb375515afb2141940a179e9f80c58dcc91eaabf2926cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "501634761d63c8090f07a2c8bc135a03aca86c89128bef28b3b10c925d37cf97",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-23T11:12:26Z",
    "title_canon_sha256": "127d987b4eb057980d38a6064cd5a6933d5677d88b640f75c7bfd2a5d22c721d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5554",
    "kind": "arxiv",
    "version": 3
  }
}