Pith Number

pith:MAJDBIMH

pith:2026:MAJDBIMHFQZUN3LROU5VGOMNO5

not attested not anchored not stored refs pending

Delaunay solutions to the fractional Hartree equation with critical growth

Jo\~{a}o Henrique Andrade, Minbo Yang, Paolo Piccione, Tao Feng

arxiv:2608.12734 v1 · 2026-08-13 · 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{MAJDBIMHFQZUN3LROU5VGOMNO5}

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	2026-08-14T00:47:17.096142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

601230a1872c3346ed71753b53398d77541bebd1b71725b6a09c24090254f970

Aliases

arxiv: 2608.12734 · arxiv_version: 2608.12734v1 · doi: 10.48550/arxiv.2608.12734 · pith_short_12: MAJDBIMHFQZU · pith_short_16: MAJDBIMHFQZUN3LR · pith_short_8: MAJDBIMH

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/MAJDBIMHFQZUN3LROU5VGOMNO5 \
  | 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: 601230a1872c3346ed71753b53398d77541bebd1b71725b6a09c24090254f970

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8099bea702eb213986709559b62380efb8554d562dd5b0d7fe4686d1e8bb823",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-13T02:29:44Z",
    "title_canon_sha256": "2ca293e78de08b8cd58880e6c75f9b22f0d71e66aad897c9eaf0d43e52d46964"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12734",
    "kind": "arxiv",
    "version": 1
  }
}