Pith Number

pith:TPHJ2W5N

pith:2011:TPHJ2W5NUYFH53ULK2D2HDTDGK

not attested not anchored not stored refs pending

Log-concavity of characteristic polynomials and the Bergman fan of matroids

Eric Katz, June Huh

arxiv:1104.2519 v2 · 2011-04-13 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPHJ2W5NUYFH53ULK2D2HDTDGK}

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	2026-05-18T04:02:15.142779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bce9d5bada60a7eee8b5687a38e6332af2efcc7128b2fd2c5c34d3a9cac5925

Aliases

arxiv: 1104.2519 · arxiv_version: 1104.2519v2 · doi: 10.48550/arxiv.1104.2519 · pith_short_12: TPHJ2W5NUYFH · pith_short_16: TPHJ2W5NUYFH53UL · pith_short_8: TPHJ2W5N

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/TPHJ2W5NUYFH53ULK2D2HDTDGK \
  | 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: 9bce9d5bada60a7eee8b5687a38e6332af2efcc7128b2fd2c5c34d3a9cac5925

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f780c351e39f0a40a5f177148eb1fb6da7173b9c4ff15c62fd376ab226b3561",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-04-13T14:51:29Z",
    "title_canon_sha256": "99864ce72ad72643b283c35d938adc6ca3ef5a8ce3251bce6aa0b7de59acf027"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2519",
    "kind": "arxiv",
    "version": 2
  }
}