Pith Number

pith:IUWLW5NB

pith:2015:IUWLW5NBY4SJ76HVMEXH76WHX2

not attested not anchored not stored refs pending

Criteria for Discrete Spectrum of 1D Operators

Mu-Fa chen

arxiv:1501.03233 v1 · 2015-01-14 · math.PR · math.AP · math.FA · 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{IUWLW5NBY4SJ76HVMEXH76WHX2}

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	2026-05-18T02:29:24.435871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

452cbb75a1c7249ff8f5612e7ffac7be926c6af2688230698cddfec7d5dd744e

Aliases

arxiv: 1501.03233 · arxiv_version: 1501.03233v1 · doi: 10.48550/arxiv.1501.03233 · pith_short_12: IUWLW5NBY4SJ · pith_short_16: IUWLW5NBY4SJ76HV · pith_short_8: IUWLW5NB

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/IUWLW5NBY4SJ76HVMEXH76WHX2 \
  | 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: 452cbb75a1c7249ff8f5612e7ffac7be926c6af2688230698cddfec7d5dd744e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8116859aa844d61c900f6f59c810dcda867e425b1eb27533a2a50a670fff289e",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-14T01:53:00Z",
    "title_canon_sha256": "afd7f6d478fe42f7ca2a48dff319c9833494b02414d3b032f4978eeb7d7d8e44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03233",
    "kind": "arxiv",
    "version": 1
  }
}