Pith Number

pith:7HNBTBTR

pith:2000:7HNBTBTRHZD3XJ2VPC3NM3L5LS

not attested not anchored not stored refs pending

Second-order linear differential equations with two irregular singular points of rank three: the characteristic exponent

Wolfgang Buehring

arxiv:math/0003148 v1 · 2000-03-24 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7HNBTBTRHZD3XJ2VPC3NM3L5LS}

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	2026-05-18T01:38:30.324814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9da1986713e47bba75578b6d66d7d5ca359d3b08b56405644ac24d0ad06446a

Aliases

arxiv: math/0003148 · arxiv_version: math/0003148v1 · doi: 10.48550/arxiv.math/0003148 · pith_short_12: 7HNBTBTRHZD3 · pith_short_16: 7HNBTBTRHZD3XJ2V · pith_short_8: 7HNBTBTR

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/7HNBTBTRHZD3XJ2VPC3NM3L5LS \
  | 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: f9da1986713e47bba75578b6d66d7d5ca359d3b08b56405644ac24d0ad06446a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21ac81d107ded4dce8b8dbb6d09e455a58ed399eeff81ff53ce6a2181a47cfbb",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2000-03-24T12:23:10Z",
    "title_canon_sha256": "3b97030c093cb155c41e4530d3de5f76b44016ebf8b293bfba564ef85f881045"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0003148",
    "kind": "arxiv",
    "version": 1
  }
}