Pith Number

pith:YBXZ7TZJ

pith:2013:YBXZ7TZJCPZNFOP5SKGQUVGDNY

not attested not anchored not stored refs pending

Graver degrees are not polynomially bounded by true circuit degrees

Apostolos Thoma, Christos Tatakis

arxiv:1306.3305 v1 · 2013-06-14 · math.AC · 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{YBXZ7TZJCPZNFOP5SKGQUVGDNY}

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	2026-05-18T00:02:14.094396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c06f9fcf2913f2d2b9fd928d0a54c36e37bc7c6652960c0ed56ba0698fbf14c7

Aliases

arxiv: 1306.3305 · arxiv_version: 1306.3305v1 · doi: 10.48550/arxiv.1306.3305 · pith_short_12: YBXZ7TZJCPZN · pith_short_16: YBXZ7TZJCPZNFOP5 · pith_short_8: YBXZ7TZJ

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/YBXZ7TZJCPZNFOP5SKGQUVGDNY \
  | 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: c06f9fcf2913f2d2b9fd928d0a54c36e37bc7c6652960c0ed56ba0698fbf14c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b112227279a10109bb4872685786bd1a8acc31e882d8078ecc984eb16b544c2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-06-14T06:33:24Z",
    "title_canon_sha256": "d0de1687a283d17380dfce151639875e5807815b326d93b73f5869e78bf2024f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3305",
    "kind": "arxiv",
    "version": 1
  }
}