Pith Number

pith:45DAQO7P

pith:2001:45DAQO7PENU7MA4X6CUOXVS7VZ

not attested not anchored not stored refs pending

Absolutely continuous spectrum of Stark operators

A. Kiselev, M. Christ

arxiv:math/0110141 v2 · 2001-10-13 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45DAQO7PENU7MA4X6CUOXVS7VZ}

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	2026-07-04T14:35:33.929934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e746083bef2369f60397f0a8ebd65fae5995be847c8233b1521711106b1ede0b

Aliases

arxiv: math/0110141 · arxiv_version: math/0110141v2 · doi: 10.48550/arxiv.math/0110141 · pith_short_12: 45DAQO7PENU7 · pith_short_16: 45DAQO7PENU7MA4X · pith_short_8: 45DAQO7P

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/45DAQO7PENU7MA4X6CUOXVS7VZ \
  | 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: e746083bef2369f60397f0a8ebd65fae5995be847c8233b1521711106b1ede0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "971196826d0211df940558a71f84874e247eb778a24279e7a47c2f8c6beabf51",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2001-10-13T21:52:00Z",
    "title_canon_sha256": "180750507419e47e98239e7dbc47a17779c5677724079b90f97bb4e37fdb87d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0110141",
    "kind": "arxiv",
    "version": 2
  }
}