Pith Number

pith:PUYRAJSI

pith:2007:PUYRAJSIZFCIQ7UBXUQCDLAUXP

not attested not anchored not stored refs pending

Gegenbauer tau methods with and without spurious eigenvalues

Fabian Waleffe, Marios Charalambides

arxiv:0708.1900 v3 · 2007-08-14 · math.NA · cs.NA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PUYRAJSIZFCIQ7UBXUQCDLAUXP}

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	2026-06-03T22:06:01.904518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d31102648c944887e81bd2021ac14bbfa85103b7228dca6552078214775f50d

Aliases

arxiv: 0708.1900 · arxiv_version: 0708.1900v3 · doi: 10.48550/arxiv.0708.1900 · pith_short_12: PUYRAJSIZFCI · pith_short_16: PUYRAJSIZFCIQ7UB · pith_short_8: PUYRAJSI

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/PUYRAJSIZFCIQ7UBXUQCDLAUXP \
  | 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: 7d31102648c944887e81bd2021ac14bbfa85103b7228dca6552078214775f50d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "157199cbb670b3a4365fbef810994fed6babd4a21c6c6d75b9385d0b052b286e",
    "cross_cats_sorted": [
      "cs.NA",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.NA",
    "submitted_at": "2007-08-14T14:38:52Z",
    "title_canon_sha256": "7235617d81c5a04d7a66d97dde3474db286a1b5399ecdf5aa8660cb26168dfa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.1900",
    "kind": "arxiv",
    "version": 3
  }
}