Pith Number

pith:DR4EQGFZ

pith:2026:DR4EQGFZIEIHSX4PFUZCC6HM67

not attested not anchored not stored refs pending

Triangle Families with Large Edge Up-Laplacian Spectral Gap

Mutasim Mim

arxiv:2605.27307 v1 · 2026-05-26 · 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{DR4EQGFZIEIHSX4PFUZCC6HM67}

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	2026-05-27T02:06:17.366774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c784818b94110795f8f2d322178ecf7db639cb8b0ea7024c39312ca29cee59c

Aliases

arxiv: 2605.27307 · arxiv_version: 2605.27307v1 · doi: 10.48550/arxiv.2605.27307 · pith_short_12: DR4EQGFZIEIH · pith_short_16: DR4EQGFZIEIHSX4P · pith_short_8: DR4EQGFZ

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/DR4EQGFZIEIHSX4PFUZCC6HM67 \
  | 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: 1c784818b94110795f8f2d322178ecf7db639cb8b0ea7024c39312ca29cee59c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c3cf1700285401f28bd1a054b17d6fa3f8115227b6d569aca1a621e33f3e96d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-26T17:18:11Z",
    "title_canon_sha256": "7ae17ff07891d0039f91434a7f3b5cb636b2153cb1fe815b7b66cc262d65a707"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.27307",
    "kind": "arxiv",
    "version": 1
  }
}