Pith Number

pith:D64MB3KC

pith:2012:D64MB3KCYMHHEIUCV5RCDONDJN

not attested not anchored not stored refs pending

Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

Kouichi Takemura, Ryu Sasaki

arxiv:1207.5302 v2 · 2012-07-23 · math.CA · hep-th · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D64MB3KCYMHHEIUCV5RCDONDJN}

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	2026-05-18T03:40:49.218068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fb8c0ed42c30e722282af6221b9a34b4ad7a4e06a2103a90bc88bae351a6a4f

Aliases

arxiv: 1207.5302 · arxiv_version: 1207.5302v2 · doi: 10.48550/arxiv.1207.5302 · pith_short_12: D64MB3KCYMHH · pith_short_16: D64MB3KCYMHHEIUC · pith_short_8: D64MB3KC

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/D64MB3KCYMHHEIUCV5RCDONDJN \
  | 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: 1fb8c0ed42c30e722282af6221b9a34b4ad7a4e06a2103a90bc88bae351a6a4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1411ff6618938bc63e6d5eaaff290f2c58a0b6b6a0797ca0db5af0acc27587c",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-07-23T06:23:00Z",
    "title_canon_sha256": "0e231e6631a09a45b3d5a427b3e73734063334ab1c02e0966e8fa67eb97497e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5302",
    "kind": "arxiv",
    "version": 2
  }
}