Pith Number

pith:HBBUDED2

pith:2025:HBBUDED2Z7FRYJL3OH2PDM2TFF

not attested not anchored not stored refs pending

Positivity, singularities, and boundedness

Caucher Birkar

arxiv:2507.18394 v1 · 2025-07-24 · 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{HBBUDED2Z7FRYJL3OH2PDM2TFF}

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	2026-07-05T11:42:47.377002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

384341907acfcb1c257b71f4f1b3532959e2fd7bbebcc62066fd6920c618028a

Aliases

arxiv: 2507.18394 · arxiv_version: 2507.18394v1 · doi: 10.48550/arxiv.2507.18394 · pith_short_12: HBBUDED2Z7FR · pith_short_16: HBBUDED2Z7FRYJL3 · pith_short_8: HBBUDED2

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/HBBUDED2Z7FRYJL3OH2PDM2TFF \
  | 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: 384341907acfcb1c257b71f4f1b3532959e2fd7bbebcc62066fd6920c618028a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de3a484350c14e18bbf41bc195a240ccf3fe4794853f814045b97c8a99f10c11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-24T13:18:42Z",
    "title_canon_sha256": "3a12c27eb41ac9d8ed3ab974cf439f174ea57b4946822801a80fc9d5dd743a21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18394",
    "kind": "arxiv",
    "version": 1
  }
}