Pith Number

pith:KOZDXB3E

pith:2015:KOZDXB3EZMVDDKHDYYWOBNDEPG

not attested not anchored not stored refs pending

Log-concavity and lower bounds for arithmetic circuits

Ignacio Garc\'ia-Marco (LIP), Pascal Koiran (LIP), S\'ebastien Tavenas

arxiv:1503.07705 v1 · 2015-03-26 · cs.CC · cs.DM · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KOZDXB3EZMVDDKHDYYWOBNDEPG}

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	2026-05-18T00:52:53.302599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53b23b8764cb2a31a8e3c62ce0b464799490c23f526e9cf88eb7a3a986dddd5e

Aliases

arxiv: 1503.07705 · arxiv_version: 1503.07705v1 · doi: 10.48550/arxiv.1503.07705 · pith_short_12: KOZDXB3EZMVD · pith_short_16: KOZDXB3EZMVDDKHD · pith_short_8: KOZDXB3E

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/KOZDXB3EZMVDDKHDYYWOBNDEPG \
  | 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: 53b23b8764cb2a31a8e3c62ce0b464799490c23f526e9cf88eb7a3a986dddd5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9e010202505fbb62c9c4d6c5c4cd887994be41e450a0df92197015df75f7f49",
    "cross_cats_sorted": [
      "cs.DM",
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-03-26T12:29:43Z",
    "title_canon_sha256": "4dfb5ecc8038edb7cdd7fb11ad9ab5a71e4748f40c0da5baa12b4fb67bf1591a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07705",
    "kind": "arxiv",
    "version": 1
  }
}