Pith Number

pith:QOEE6ZUU

pith:2011:QOEE6ZUULLU7H3T7FB25VI2MKO

not attested not anchored not stored refs pending

Behaviors of $\phi$-exponential distributions in Wasserstein geometry and an evolution equation

Asuka Takatsu

arxiv:1109.6776 v1 · 2011-09-30 · math.MG · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QOEE6ZUULLU7H3T7FB25VI2MKO}

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	2026-05-18T04:11:52.510875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83884f66945ae9f3ee7f2875daa34c53bde0543097c0e2d1856b8635fba4e2a6

Aliases

arxiv: 1109.6776 · arxiv_version: 1109.6776v1 · doi: 10.48550/arxiv.1109.6776 · pith_short_12: QOEE6ZUULLU7 · pith_short_16: QOEE6ZUULLU7H3T7 · pith_short_8: QOEE6ZUU

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/QOEE6ZUULLU7H3T7FB25VI2MKO \
  | 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: 83884f66945ae9f3ee7f2875daa34c53bde0543097c0e2d1856b8635fba4e2a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac2b7ed5ae6023ede5f54b601d8691b05dfa185a1181922e53241e72f7f88e12",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-09-30T09:59:35Z",
    "title_canon_sha256": "51b75a8e3159313bd73f3d3bb45bf0dcdd5d461829f4ead7b784bd5a10c1be28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6776",
    "kind": "arxiv",
    "version": 1
  }
}