Pith Number

pith:53JUY277

pith:2008:53JUY277LIOUMGQ2MMNEBNMELB

not attested not anchored not stored refs pending

Polynomial hierarchy, Betti numbers and a real analogue of Toda's theorem

Saugata Basu, Thierry Zell

arxiv:0812.1200 v3 · 2008-12-05 · cs.CC · math.AT · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{53JUY277LIOUMGQ2MMNEBNMELB}

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	2026-05-18T04:30:14.784038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eed34c6bff5a1d461a1a631a40b584584e469877613b658a3925f4feb7a0a043

Aliases

arxiv: 0812.1200 · arxiv_version: 0812.1200v3 · doi: 10.48550/arxiv.0812.1200 · pith_short_12: 53JUY277LIOU · pith_short_16: 53JUY277LIOUMGQ2 · pith_short_8: 53JUY277

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/53JUY277LIOUMGQ2MMNEBNMELB \
  | 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: eed34c6bff5a1d461a1a631a40b584584e469877613b658a3925f4feb7a0a043

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddafc045a7389419a0e9d012883c02daf04b2159d466fe0c323d250545e54764",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2008-12-05T19:09:27Z",
    "title_canon_sha256": "4aa110d1fe54d03481e541e074e6e17acbc923adf000595469eda74a60e18c82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1200",
    "kind": "arxiv",
    "version": 3
  }
}