Pith Number

pith:67KODJQ7

pith:2019:67KODJQ7HTYL2W7QXJTFW725QP

not attested not anchored not stored refs pending

The general spectral radius and majorization theorem of $t$-cone graphs with given degree sequences

Muhuo Liu, Yufei Huang

arxiv:1908.06224 v1 · 2019-08-17 · 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{67KODJQ7HTYL2W7QXJTFW725QP}

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	2026-07-04T23:58:13.559389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7d4e1a61f3cf0bd5bf0ba665b7f5d83ec8770928abcdb4b8827d0c4b2b09b9b

Aliases

arxiv: 1908.06224 · arxiv_version: 1908.06224v1 · doi: 10.48550/arxiv.1908.06224 · pith_short_12: 67KODJQ7HTYL · pith_short_16: 67KODJQ7HTYL2W7Q · pith_short_8: 67KODJQ7

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/67KODJQ7HTYL2W7QXJTFW725QP \
  | 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: f7d4e1a61f3cf0bd5bf0ba665b7f5d83ec8770928abcdb4b8827d0c4b2b09b9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "106d212ace3b5adbcc46ea577ec822b0a166e6782976437c4b07f9db2c18ccbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-17T02:14:04Z",
    "title_canon_sha256": "992344686ee3071afa9432ccb6944f8616fc29b1be7406b1eab1d6a382762157"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06224",
    "kind": "arxiv",
    "version": 1
  }
}