Pith Number

pith:TH5G6JJH

pith:2026:TH5G6JJHNJSEKN5MTSRZL3VVDX

not attested not anchored not stored refs pending

Restriction estimates for toral eigenfunctions and lattice points in spherical regions

Cheng Zhang, Zhifei Zhu

arxiv:2606.08650 v1 · 2026-06-07 · math.AP · math.CA · math.NT · 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{TH5G6JJHNJSEKN5MTSRZL3VVDX}

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	2026-06-09T01:05:42.711218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99fa6f25276a644537ac9ca395eeb51dcb7ffdbda19b2b7aecf686b28a1dc910

Aliases

arxiv: 2606.08650 · arxiv_version: 2606.08650v1 · doi: 10.48550/arxiv.2606.08650 · pith_short_12: TH5G6JJHNJSE · pith_short_16: TH5G6JJHNJSEKN5M · pith_short_8: TH5G6JJH

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/TH5G6JJHNJSEKN5MTSRZL3VVDX \
  | 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: 99fa6f25276a644537ac9ca395eeb51dcb7ffdbda19b2b7aecf686b28a1dc910

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d30e4a5b722f1101df95fc624f37c84aeaa3a7e16dbddf74ca594fa1ed6a369",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-07T14:32:12Z",
    "title_canon_sha256": "500f7a23ed550aa72b6aed2d40ccc7974cb37d54ee7681a87cb0cb57849dbf51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08650",
    "kind": "arxiv",
    "version": 1
  }
}