Pith Number

pith:7FYTUHSN

pith:2016:7FYTUHSNP7CNGOM3GMJMUBC7RK

not attested not anchored not stored refs pending

The asymptotic trace norm of random circulants and the graph energy

Sergiy Koshkin

arxiv:1610.02449 v1 · 2016-10-07 · math.PR · 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{7FYTUHSNP7CNGOM3GMJMUBC7RK}

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	2026-05-18T01:02:51.474303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9713a1e4d7fc4d3399b3312ca045f8a8d816d5a238ec4678b26b7b76918c496

Aliases

arxiv: 1610.02449 · arxiv_version: 1610.02449v1 · doi: 10.48550/arxiv.1610.02449 · pith_short_12: 7FYTUHSNP7CN · pith_short_16: 7FYTUHSNP7CNGOM3 · pith_short_8: 7FYTUHSN

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/7FYTUHSNP7CNGOM3GMJMUBC7RK \
  | 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: f9713a1e4d7fc4d3399b3312ca045f8a8d816d5a238ec4678b26b7b76918c496

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b30c5b4365552bd314b8be63b8bb70d2ba48e45dfb678865d0af214f78ddc1b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-07T23:56:20Z",
    "title_canon_sha256": "4959203130678e162757d8c052f2bdbdaab58d5854514ba6a37f2a31d0fb690b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02449",
    "kind": "arxiv",
    "version": 1
  }
}