Pith Number

pith:KFM7DQOE

pith:2025:KFM7DQOEAIFNKGZOUDMZUKWJGR

not attested not anchored not stored refs pending

Dold-Gauss Congruences, Norm Descent, and Rational Rigidity

Hartosh Singh Bal

arxiv:2509.25038 v2 · 2025-09-29 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KFM7DQOEAIFNKGZOUDMZUKWJGR}

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	2026-06-04T01:08:32.531474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5159f1c1c4020ad51b2ea0d99a2ac93452007b17e79f36ef73d9d3f884833c6e

Aliases

arxiv: 2509.25038 · arxiv_version: 2509.25038v2 · doi: 10.48550/arxiv.2509.25038 · pith_short_12: KFM7DQOEAIFN · pith_short_16: KFM7DQOEAIFNKGZO · pith_short_8: KFM7DQOE

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/KFM7DQOEAIFNKGZOUDMZUKWJGR \
  | 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: 5159f1c1c4020ad51b2ea0d99a2ac93452007b17e79f36ef73d9d3f884833c6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "095c7ed0a16a74461d8f2664c1f2e74d7ae883fdb8e24e60f6a15cd455421636",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-09-29T16:56:20Z",
    "title_canon_sha256": "630cd972eb326de4406d606473890ae1b5ec0004e9b7d0cd2b84f291e81b1ffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.25038",
    "kind": "arxiv",
    "version": 2
  }
}