Pith Number

pith:A3MLWWDI

pith:2025:A3MLWWDIUOWMRGGSKO42MTVS6X

not attested not anchored not stored refs pending

Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels

Konstantin Merz, Krzysztof Bogdan

arxiv:2506.08115 v1 · 2025-06-09 · math.AP · math.FA · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A3MLWWDIUOWMRGGSKO42MTVS6X}

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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.

Cited by

1 paper in Pith

Sharp upper bounds for the density of relativistic atoms: Noninteracting case

Receipt and verification

First computed	2026-07-05T11:18:44.957033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06d8bb5868a3acc898d253b9a64eb2f5ef38927509ea30a63ab89411b86540f9

Aliases

arxiv: 2506.08115 · arxiv_version: 2506.08115v1 · doi: 10.48550/arxiv.2506.08115 · pith_short_12: A3MLWWDIUOWM · pith_short_16: A3MLWWDIUOWMRGGS · pith_short_8: A3MLWWDI

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/A3MLWWDIUOWMRGGSKO42MTVS6X \
  | 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: 06d8bb5868a3acc898d253b9a64eb2f5ef38927509ea30a63ab89411b86540f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae39accf8861a543db67be2cd606877d4ac96ed8b2c680b0750da6a79b055deb",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-09T18:14:52Z",
    "title_canon_sha256": "a76f8368b46d00b998344b9e392bfaf5abced612f44950ac9a2698c2604b4c1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08115",
    "kind": "arxiv",
    "version": 1
  }
}