Pith Number

pith:PLRMVCFE

pith:2011:PLRMVCFEGBBHZTCUNZUKFGH7S4

not attested not anchored not stored refs pending

Representations of almost periodic pseudodifferential operators and applications in spectral theory

Patrik Wahlberg

arxiv:1104.4851 v1 · 2011-04-26 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLRMVCFEGBBHZTCUNZUKFGH7S4}

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	2026-05-18T04:23:32.873650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ae2ca88a430427ccc546e68a298ff97376f1aeadc1ad89a7330cc4659e6d449

Aliases

arxiv: 1104.4851 · arxiv_version: 1104.4851v1 · doi: 10.48550/arxiv.1104.4851 · pith_short_12: PLRMVCFEGBBH · pith_short_16: PLRMVCFEGBBHZTCU · pith_short_8: PLRMVCFE

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/PLRMVCFEGBBHZTCUNZUKFGH7S4 \
  | 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: 7ae2ca88a430427ccc546e68a298ff97376f1aeadc1ad89a7330cc4659e6d449

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1444a24687e639a27dfa1e5ccd2f6883a1efc26891b694c4d5009fd244d10371",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-04-26T07:27:17Z",
    "title_canon_sha256": "129ffde0ebc0ab8411363001f00364638226bd63b301267f8c9692f06c8e7014"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4851",
    "kind": "arxiv",
    "version": 1
  }
}