Pith Number

pith:CHHNR4HQ

pith:2012:CHHNR4HQXTFGQDOBVKG7IKBI5V

not attested not anchored not stored refs pending

A Sharpened Condition for Strict Log-Convexity of the Spectral Radius via the Bipartite Graph

Lee Altenberg

arxiv:1208.1036 v2 · 2012-08-05 · math.SP · 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{CHHNR4HQXTFGQDOBVKG7IKBI5V}

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	2026-05-18T03:34:48.259830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11ced8f0f0bcca680dc1aa8df42828ed4fd9e414678bcbcd0b60fe9c8c946e4b

Aliases

arxiv: 1208.1036 · arxiv_version: 1208.1036v2 · doi: 10.48550/arxiv.1208.1036 · pith_short_12: CHHNR4HQXTFG · pith_short_16: CHHNR4HQXTFGQDOB · pith_short_8: CHHNR4HQ

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/CHHNR4HQXTFGQDOBVKG7IKBI5V \
  | 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: 11ced8f0f0bcca680dc1aa8df42828ed4fd9e414678bcbcd0b60fe9c8c946e4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "500e50af4298ddf29a1523b2671d9abd61ee9428c639e626dcfbe1af9b1659a1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-08-05T16:52:11Z",
    "title_canon_sha256": "436efd564a34ebe314e7a651fc6780d426f48ecb5830d80b3bf9bd8df9271a71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1036",
    "kind": "arxiv",
    "version": 2
  }
}