Pith Number

pith:OTXYAVUB

pith:2009:OTXYAVUBPWU77H42Y547L2VCGZ

not attested not anchored not stored refs pending

On $\gamma$-vectors satisfying the Kruskal-Katona inequalities

Eran Nevo, T. Kyle Petersen

arxiv:0909.0694 v3 · 2009-09-03 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OTXYAVUBPWU77H42Y547L2VCGZ}

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	2026-05-18T04:16:10.793456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74ef8056817da9ff9f9ac779f5eaa23663bf66cb1dddf96fee47d5eaea131c9e

Aliases

arxiv: 0909.0694 · arxiv_version: 0909.0694v3 · doi: 10.48550/arxiv.0909.0694 · pith_short_12: OTXYAVUBPWU7 · pith_short_16: OTXYAVUBPWU77H42 · pith_short_8: OTXYAVUB

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/OTXYAVUBPWU77H42Y547L2VCGZ \
  | 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: 74ef8056817da9ff9f9ac779f5eaa23663bf66cb1dddf96fee47d5eaea131c9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6215dac3305472f832beeb0809fb61d64eb1256a52eaf4fcb0400c21f4dfac9f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-09-03T15:58:13Z",
    "title_canon_sha256": "c742e3177fb6d06f39b30544108e4a26dc961ee6f4405f576e1bd2e2f4acf5ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0694",
    "kind": "arxiv",
    "version": 3
  }
}