Pith Number

pith:TBOTA3WH

pith:2010:TBOTA3WHQVXRI2BKVYJNYCJ6HH

not attested not anchored not stored refs pending

Relative log-concavity and a pair of triangle inequalities

Yaming Yu

arxiv:1010.2043 v1 · 2010-10-11 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TBOTA3WHQVXRI2BKVYJNYCJ6HH}

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	2026-05-18T04:39:29.840145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

985d306ec7856f14682aae12dc093e39d7fe703bde02f741fa784ac53cd7bbb0

Aliases

arxiv: 1010.2043 · arxiv_version: 1010.2043v1 · doi: 10.48550/arxiv.1010.2043 · pith_short_12: TBOTA3WHQVXR · pith_short_16: TBOTA3WHQVXRI2BK · pith_short_8: TBOTA3WH

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/TBOTA3WHQVXRI2BKVYJNYCJ6HH \
  | 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: 985d306ec7856f14682aae12dc093e39d7fe703bde02f741fa784ac53cd7bbb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80c5b55f48a434af80a0eee0df26e1e17b38e6d2718706f96987b27ffb6a6310",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2010-10-11T09:09:53Z",
    "title_canon_sha256": "9f9aa413a293a889e40a1e7bbaf9488352a7a192fa204a04a667abde31a6a087"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2043",
    "kind": "arxiv",
    "version": 1
  }
}