Pith Number

pith:3JGMLBWE

pith:2019:3JGMLBWEBKRF6LIIEEF2HMUTPR

not attested not anchored not stored refs pending

Asymptotic expantion of covariant symbol on the complex unit sphere

Erik I. D\'iaz-Ort\'iz

arxiv:1907.02139 v2 · 2019-07-03 · math.CV · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3JGMLBWEBKRF6LIIEEF2HMUTPR}

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	2026-05-17T23:41:16.939277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da4cc586c40aa25f2d08210ba3b2937c41c1635e24c38a2df5c871e7888fae70

Aliases

arxiv: 1907.02139 · arxiv_version: 1907.02139v2 · doi: 10.48550/arxiv.1907.02139 · pith_short_12: 3JGMLBWEBKRF · pith_short_16: 3JGMLBWEBKRF6LII · pith_short_8: 3JGMLBWE

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/3JGMLBWEBKRF6LIIEEF2HMUTPR \
  | 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: da4cc586c40aa25f2d08210ba3b2937c41c1635e24c38a2df5c871e7888fae70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e122464a660b5ae19917558b3b8ca6ad6a43fd3ee90f44f7212e9618e669f2c4",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2019-07-03T21:37:50Z",
    "title_canon_sha256": "3c688974363adda96b9c75fd9bc66684988bd463ca31f3297b8f6af389f2d4f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.02139",
    "kind": "arxiv",
    "version": 2
  }
}