Pith Number

pith:FCLBZDSU

pith:2026:FCLBZDSU3QCR4QYPJW23H2JLBN

not attested not anchored not stored refs pending

Path-Minimality for Positive $p$-Energies, Laplacian-Type Spectra, and Line Graphs

Quanyu Tang, Yinchen Liu

arxiv:2606.30996 v1 · 2026-06-30 · 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{FCLBZDSU3QCR4QYPJW23H2JLBN}

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	2026-07-01T00:17:23.774902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28961c8e54dc051e430f4db5b3e92b0b7be243482c926adf400775ebd25b20fc

Aliases

arxiv: 2606.30996 · arxiv_version: 2606.30996v1 · doi: 10.48550/arxiv.2606.30996 · pith_short_12: FCLBZDSU3QCR · pith_short_16: FCLBZDSU3QCR4QYP · pith_short_8: FCLBZDSU

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/FCLBZDSU3QCR4QYPJW23H2JLBN \
  | 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: 28961c8e54dc051e430f4db5b3e92b0b7be243482c926adf400775ebd25b20fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e5f818eb915dea9681691867d82afb7539edc4ae525483120acfd14b4e315c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-30T00:15:02Z",
    "title_canon_sha256": "8ddf2fef02adbafd76f4bc266048f211caa6faf71b3d7ecc83de7fe434f71061"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30996",
    "kind": "arxiv",
    "version": 1
  }
}