Pith Number

pith:FVGMA72T

pith:2024:FVGMA72TDJUCOOMRCHB5FV75RT

not attested not anchored not stored refs pending

Spectral extremal results on the $A_\alpha$-spectral radius of graphs without $K_{a,b}$-minor

Shuchao Li, Xingyu Lei

arxiv:2412.06399 v1 · 2024-12-09 · 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{FVGMA72TDJUCOOMRCHB5FV75RT}

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	2026-07-05T09:46:20.171253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d4cc07f531a6827399111c3d2d7fd8cd8a59329d09b9eb73fde54fdbb136447

Aliases

arxiv: 2412.06399 · arxiv_version: 2412.06399v1 · doi: 10.48550/arxiv.2412.06399 · pith_short_12: FVGMA72TDJUC · pith_short_16: FVGMA72TDJUCOOMR · pith_short_8: FVGMA72T

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/FVGMA72TDJUCOOMRCHB5FV75RT \
  | 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: 2d4cc07f531a6827399111c3d2d7fd8cd8a59329d09b9eb73fde54fdbb136447

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93c90dc8a9b208aa84939ec38be9597d745b2c3af4ae6e898518524172fcb6d0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-09T11:30:16Z",
    "title_canon_sha256": "9a4fd781e31b0193920bee1b830040f343ad68f2fc6b17a751fd0b4c50acc61b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.06399",
    "kind": "arxiv",
    "version": 1
  }
}