Pith Number

pith:S2564AOS

pith:2024:S2564AOSSAEBOBKP4GIPHE7CR5

not attested not anchored not stored refs pending

Semiclassical measure of the spherical harmonics by Bourgain on $\mathbb{S}^3$

Xiaolong Han

arxiv:2411.08146 v1 · 2024-11-12 · math.CA · math.AP · 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{S2564AOSSAEBOBKP4GIPHE7CR5}

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	2026-07-05T09:34:42.009613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96bbee01d2900817054fe190f393e28f5b94e1360278f683be7f2f65a4cf51d4

Aliases

arxiv: 2411.08146 · arxiv_version: 2411.08146v1 · doi: 10.48550/arxiv.2411.08146 · pith_short_12: S2564AOSSAEB · pith_short_16: S2564AOSSAEBOBKP · pith_short_8: S2564AOS

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/S2564AOSSAEBOBKP4GIPHE7CR5 \
  | 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: 96bbee01d2900817054fe190f393e28f5b94e1360278f683be7f2f65a4cf51d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f316c7c366588e844e56b91f56534e4dde16a9a791c25b0f7ddc03a4a3fa8df4",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2024-11-12T19:49:11Z",
    "title_canon_sha256": "3ed12ec902c57519ea450eb43b5ad9a138173d9ec8af066d14846187e5a917f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.08146",
    "kind": "arxiv",
    "version": 1
  }
}