Pith Number

pith:2WANBHZU

pith:2018:2WANBHZUMY7CZBW5VGVUYLFUFF

not attested not anchored not stored refs pending

The stability of a Cosine-Sine Functional Equation on abelian groups

Ajebbar Omar, Elqorachi Elhoucien, Themistocles M. Rassias

arxiv:1810.10295 v1 · 2018-10-24 · math.AC · 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{2WANBHZUMY7CZBW5VGVUYLFUFF}

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	2026-05-18T00:02:23.612728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d580d09f34663e2c86dda9ab4c2cb429626f06e6dcbe383d40f234f5b11e1a9d

Aliases

arxiv: 1810.10295 · arxiv_version: 1810.10295v1 · doi: 10.48550/arxiv.1810.10295 · pith_short_12: 2WANBHZUMY7C · pith_short_16: 2WANBHZUMY7CZBW5 · pith_short_8: 2WANBHZU

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/2WANBHZUMY7CZBW5VGVUYLFUFF \
  | 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: d580d09f34663e2c86dda9ab4c2cb429626f06e6dcbe383d40f234f5b11e1a9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62de10ef5dcadfd9412a2b62edc1b78e55676276241169d38d4c74c1f04eca8d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-10-24T11:14:15Z",
    "title_canon_sha256": "206637360b9df60b468e66475373b974bbccf862e03f5515d793e11133ad1a67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.10295",
    "kind": "arxiv",
    "version": 1
  }
}