Pith Number

pith:QYKJX2ZL

pith:2016:QYKJX2ZLVWENEAM3PK7MSVE72T

not attested not anchored not stored refs pending

Counterexamples to the Complement Problem

Pierre-Marie Poloni

arxiv:1605.05169 v4 · 2016-05-17 · 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{QYKJX2ZLVWENEAM3PK7MSVE72T}

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	2026-05-18T00:51:01.308702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86149beb2bad88d2019b7abec9549fd4fa5d102a07a9af5bd82d7a404b121c7f

Aliases

arxiv: 1605.05169 · arxiv_version: 1605.05169v4 · doi: 10.48550/arxiv.1605.05169 · pith_short_12: QYKJX2ZLVWEN · pith_short_16: QYKJX2ZLVWENEAM3 · pith_short_8: QYKJX2ZL

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/QYKJX2ZLVWENEAM3PK7MSVE72T \
  | 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: 86149beb2bad88d2019b7abec9549fd4fa5d102a07a9af5bd82d7a404b121c7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a869585f26173e1f0ab8715341a851c4d7dc5c986e6594ba09290ee859f8d284",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-05-17T14:04:09Z",
    "title_canon_sha256": "d1e6a6c9bba3cd9dd394182e0cd889451713efaa86c65b005a0e8ef4bb4195da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05169",
    "kind": "arxiv",
    "version": 4
  }
}