Pith Number

pith:VSY2WPTZ

pith:2025:VSY2WPTZK7JSFY2IZOS4KE4KYT

not attested not anchored not stored refs pending

Expansion of a bivariate symmetric mean in the neighborhood of the first bisector

Bakir Farhi

arxiv:2506.07601 v1 · 2025-06-09 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VSY2WPTZK7JSFY2IZOS4KE4KYT}

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	2026-07-05T11:18:30.157244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acb1ab3e7957d322e348cba5c5138ac4c50f08eb16ddfe17dc401b83b12ee2d3

Aliases

arxiv: 2506.07601 · arxiv_version: 2506.07601v1 · doi: 10.48550/arxiv.2506.07601 · pith_short_12: VSY2WPTZK7JS · pith_short_16: VSY2WPTZK7JSFY2I · pith_short_8: VSY2WPTZ

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/VSY2WPTZK7JSFY2IZOS4KE4KYT \
  | 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: acb1ab3e7957d322e348cba5c5138ac4c50f08eb16ddfe17dc401b83b12ee2d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66c9c79332d74c590fd2466f0217a111dc91015ed97aa8695223dc17a5d5203b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-09T10:01:07Z",
    "title_canon_sha256": "9376bb3617087c0a9a1a2e4297ce0c0f1fa97f1cb8ba7086f6f3cf699e9098c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07601",
    "kind": "arxiv",
    "version": 1
  }
}