Pith Number

pith:72FFGHTT

pith:2025:72FFGHTT4L65IXRCHJDIEF5SZW

not attested not anchored not stored refs pending

Solutions with clustering concentration layers to the Ambrosetti-Prodi type problem

Qiang Ren

arxiv:2512.21600 v2 · 2025-12-25 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72FFGHTT4L65IXRCHJDIEF5SZW}

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	2026-05-20T00:04:19.482116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe8a531e73e2fdd45e223a468217b2cdb81786bcf4d534fbdf6055e492489415

Aliases

arxiv: 2512.21600 · arxiv_version: 2512.21600v2 · doi: 10.48550/arxiv.2512.21600 · pith_short_12: 72FFGHTT4L65 · pith_short_16: 72FFGHTT4L65IXRC · pith_short_8: 72FFGHTT

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/72FFGHTT4L65IXRCHJDIEF5SZW \
  | 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: fe8a531e73e2fdd45e223a468217b2cdb81786bcf4d534fbdf6055e492489415

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cbb4a9ad8d88ce258738292ac8656dcc7e6fa7889622dc95c5be22c1b4b5e56",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-12-25T09:43:46Z",
    "title_canon_sha256": "5927e3112b7f0b4ea0d920fb74ecdc0209d7028c613175e6d1384a3ba069ecc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.21600",
    "kind": "arxiv",
    "version": 2
  }
}