Pith Number

pith:5ST7ANKL

pith:2025:5ST7ANKLFB2BS7L5FM7PKYOARE

not attested not anchored not stored refs pending

Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory

Philip Isett, Sung-Jin Oh, Yuchen Mao, Zhongkai Tao

arxiv:2509.04617 v1 · 2025-09-04 · math.AP · gr-qc · 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{5ST7ANKLFB2BS7L5FM7PKYOARE}

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	2026-07-05T12:05:26.354502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eca7f0354b2874197d7d2b3ef561c089073fa833c39aa9b57f4985ecc4cfef6c

Aliases

arxiv: 2509.04617 · arxiv_version: 2509.04617v1 · doi: 10.48550/arxiv.2509.04617 · pith_short_12: 5ST7ANKLFB2B · pith_short_16: 5ST7ANKLFB2BS7L5 · pith_short_8: 5ST7ANKL

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/5ST7ANKLFB2BS7L5FM7PKYOARE \
  | 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: eca7f0354b2874197d7d2b3ef561c089073fa833c39aa9b57f4985ecc4cfef6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5822c85348e81944f7f0522f802d2f2d850289ea304469932fa84d2a59f028be",
    "cross_cats_sorted": [
      "gr-qc",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-04T19:02:03Z",
    "title_canon_sha256": "fa9d0340f25a3a802137056996bd9f7911982c477a4d1fc0a6b942e893f34f08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.04617",
    "kind": "arxiv",
    "version": 1
  }
}