Pith Number

pith:HRPGZD3R

pith:2013:HRPGZD3RLZUNJWQOHACJ2B2UNW

not attested not anchored not stored refs pending

The Sobolev norms and localization on the Fourier side for the solutions to some evolution equations

Sergey A. Denisov

arxiv:1306.3178 v2 · 2013-06-13 · math.AP · 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{HRPGZD3RLZUNJWQOHACJ2B2UNW}

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	2026-05-18T02:56:59.902138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666

Aliases

arxiv: 1306.3178 · arxiv_version: 1306.3178v2 · doi: 10.48550/arxiv.1306.3178 · pith_short_12: HRPGZD3RLZUN · pith_short_16: HRPGZD3RLZUNJWQO · pith_short_8: HRPGZD3R

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/HRPGZD3RLZUNJWQOHACJ2B2UNW \
  | 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: 3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "306ff5fd7cfb51f46c74b4db2143fc395eaaa92bd9a7f389134675b3c59b0521",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-13T18:04:05Z",
    "title_canon_sha256": "52c3378d5ffe63b4c349811fdc1b6badd457d4c01e07e20d0805fd5568abcce3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3178",
    "kind": "arxiv",
    "version": 2
  }
}