Pith Number

pith:H4NYT3M6

pith:2025:H4NYT3M63ZL5ACLVGDZHDXZRB4

not attested not anchored not stored refs pending

Numerical Reduction and Sharp Thresholds for Adjoint Singularities of Foliated Surfaces

Shi Xu

arxiv:2512.20744 v3 · 2025-12-23 · 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{H4NYT3M63ZL5ACLVGDZHDXZRB4}

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.

Cited by

1 paper in Pith

Birational boundedness of stable families

Receipt and verification

First computed	2026-06-30T01:17:31.564742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f1b89ed9ede57d0097530f271df310f2ab5140fc1c4682b10c7be8fb62add79

Aliases

arxiv: 2512.20744 · arxiv_version: 2512.20744v3 · doi: 10.48550/arxiv.2512.20744 · pith_short_12: H4NYT3M63ZL5 · pith_short_16: H4NYT3M63ZL5ACLV · pith_short_8: H4NYT3M6

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/H4NYT3M63ZL5ACLVGDZHDXZRB4 \
  | 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: 3f1b89ed9ede57d0097530f271df310f2ab5140fc1c4682b10c7be8fb62add79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a7a3c331c880fcd617354f525e8233eaa4f774f663bb8dfbd7df45673687017",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-12-23T19:56:31Z",
    "title_canon_sha256": "fb3e6c1056cdc2ab529ebd4091f547ba59699c3fc0f3d05444b893fdd3191998"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.20744",
    "kind": "arxiv",
    "version": 3
  }
}