Pith Number

pith:MWIUENMF

pith:2026:MWIUENMFTW73ZHQRRQBJMP3NQ6

not attested not anchored not stored refs pending

On the minimal model theory for generalized pairs of relative log numerical dimension zero

Cheng Zhang

arxiv:2606.09087 v1 · 2026-06-08 · 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{MWIUENMFTW73ZHQRRQBJMP3NQ6}

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	2026-06-09T02:07:58.203515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65914235859dbfbc9e118c02963f6d8786022c0120118d6fa9f5b3d32c7ecc5c

Aliases

arxiv: 2606.09087 · arxiv_version: 2606.09087v1 · doi: 10.48550/arxiv.2606.09087 · pith_short_12: MWIUENMFTW73 · pith_short_16: MWIUENMFTW73ZHQR · pith_short_8: MWIUENMF

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/MWIUENMFTW73ZHQRRQBJMP3NQ6 \
  | 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: 65914235859dbfbc9e118c02963f6d8786022c0120118d6fa9f5b3d32c7ecc5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00f1ce24a1543fa3673e7ba17f49e09545382d94f1050023a92e44666f24fc3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-06-08T06:33:56Z",
    "title_canon_sha256": "e892f5399ac38991a32000c86624b66a22014f356d8d3ecaa77f4f36fd429dad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09087",
    "kind": "arxiv",
    "version": 1
  }
}