Pith Number

pith:3N5PO3W5

pith:2026:3N5PO3W5T52S6OMVR2UPSTWSR2

not attested not anchored not stored refs pending

Minimum second neighborhood degree energy of commuting graphs of finite rings

Jutirekha Dutta, Payal Tak, Rajat Kanti Nath

arxiv:2605.22160 v1 · 2026-05-21 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3N5PO3W5T52S6OMVR2UPSTWSR2}

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	2026-05-22T01:04:29.175507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db7af76edd9f752f39958ea8f94ed28ea0f16ff4cec71a26e99868cbd583e921

Aliases

arxiv: 2605.22160 · arxiv_version: 2605.22160v1 · doi: 10.48550/arxiv.2605.22160 · pith_short_12: 3N5PO3W5T52S · pith_short_16: 3N5PO3W5T52S6OMV · pith_short_8: 3N5PO3W5

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/3N5PO3W5T52S6OMVR2UPSTWSR2 \
  | 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: db7af76edd9f752f39958ea8f94ed28ea0f16ff4cec71a26e99868cbd583e921

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4913ad465f2b37a2499e948a1b5a0b2ff13473b5099a8252dfaa936f9a026954",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-05-21T08:29:20Z",
    "title_canon_sha256": "13752f038f990e706050fb2e53d5abed7cef09297606b7487df4947fcf8ff9e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22160",
    "kind": "arxiv",
    "version": 1
  }
}