Pith Number

pith:YGIRBKY2

pith:2000:YGIRBKY2PVQ6BVPBV227EMKHDC

not attested not anchored not stored refs pending

Some spherical uniqueness theorems for multiple trigonometric series

Gang Wang, J. Marshall Ash

arxiv:math/0008031 v1 · 2000-08-03 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YGIRBKY2PVQ6BVPBV227EMKHDC}

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	2026-07-04T14:34:37.780245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c19110ab1a7d61e0d5e1aeb5f23147188becf0c5f7316f0a41f58ce1c32e7ec2

Aliases

arxiv: math/0008031 · arxiv_version: math/0008031v1 · doi: 10.48550/arxiv.math/0008031 · pith_short_12: YGIRBKY2PVQ6 · pith_short_16: YGIRBKY2PVQ6BVPB · pith_short_8: YGIRBKY2

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/YGIRBKY2PVQ6BVPBV227EMKHDC \
  | 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: c19110ab1a7d61e0d5e1aeb5f23147188becf0c5f7316f0a41f58ce1c32e7ec2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22148831d3289f905eadd96b1723cc46a5f50b720e3881c6b2bdbbe17a8110c4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2000-08-03T16:28:03Z",
    "title_canon_sha256": "182613df5d6e9e9d905068a1e90d0a192de8a78cf686ed6e9a4dbbcd6693dc4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008031",
    "kind": "arxiv",
    "version": 1
  }
}