Pith Number

pith:7CLGPVY2

pith:2025:7CLGPVY27CBDV6IF7LIM5W5NUM

not attested not anchored not stored refs pending

A Baseline $T\log^2 T$ Upper Bound for KL-Regularized Prime--Zero Optimal Transport

Zhejun Yang (University of Sydney)

arxiv:2509.07329 v1 · 2025-09-09 · math.NT · math.CA · 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{7CLGPVY27CBDV6IF7LIM5W5NUM}

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	2026-07-05T12:07:19.637875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f89667d71af8823af905fad0cedbada3189fa60f10e95ff991e7d51469e7cd9b

Aliases

arxiv: 2509.07329 · arxiv_version: 2509.07329v1 · doi: 10.48550/arxiv.2509.07329 · pith_short_12: 7CLGPVY27CBD · pith_short_16: 7CLGPVY27CBDV6IF · pith_short_8: 7CLGPVY2

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/7CLGPVY27CBDV6IF7LIM5W5NUM \
  | 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: f89667d71af8823af905fad0cedbada3189fa60f10e95ff991e7d51469e7cd9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d51c275e2c39bb33a846eabbb507bd93fbaec9676fe316cd691a6d21e00524bd",
    "cross_cats_sorted": [
      "math.CA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-09T01:54:30Z",
    "title_canon_sha256": "c8ef02378438497d46cbd9f2fc48376dd953f28a16ec18fc48729f4faf6c49e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07329",
    "kind": "arxiv",
    "version": 1
  }
}