Pith Number

pith:XWGZLAMG

pith:2026:XWGZLAMG4QIVSMR6IIY7OOGTE6

not attested not anchored not stored refs pending

Path-Minimality of $p$-Energy for Connected Graphs

Quanyu Tang, Yinchen Liu

arxiv:2605.22730 v1 · 2026-05-21 · 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{XWGZLAMG4QIVSMR6IIY7OOGTE6}

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	2026-05-22T02:04:52.322760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd8d958186e41159323e4231f738d32790506a86db43b9012d4e07e28745dca8

Aliases

arxiv: 2605.22730 · arxiv_version: 2605.22730v1 · doi: 10.48550/arxiv.2605.22730 · pith_short_12: XWGZLAMG4QIV · pith_short_16: XWGZLAMG4QIVSMR6 · pith_short_8: XWGZLAMG

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/XWGZLAMG4QIVSMR6IIY7OOGTE6 \
  | 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: bd8d958186e41159323e4231f738d32790506a86db43b9012d4e07e28745dca8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8638eae7f862351b7c487f227d8bc095468fbf0ee1823097ad5963cb9b56ecf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-21T17:03:10Z",
    "title_canon_sha256": "95127cc3b6ec56cfedecd54a0b4c063b39d012a99be99afd189c691a71f809cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22730",
    "kind": "arxiv",
    "version": 1
  }
}