Pith Number

pith:ZMKJABSE

pith:2024:ZMKJABSEYRP5IRZ52MVSH6K7S7

not attested not anchored not stored refs pending

Optimal Eigenvalue Rigidity of Random Regular Graphs

Horng-Tzer Yau, Jiaoyang Huang, Theo McKenzie

arxiv:2405.12161 v1 · 2024-05-20 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZMKJABSEYRP5IRZ52MVSH6K7S7}

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.

Cited by

1 paper in Pith

Ramanujan Graphs and Interlacing Families

Receipt and verification

First computed	2026-07-05T08:21:00.910474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb14900644c45fd4473dd32b23f95f97c27305cc5c3521cdd5a794ba74568dea

Aliases

arxiv: 2405.12161 · arxiv_version: 2405.12161v1 · doi: 10.48550/arxiv.2405.12161 · pith_short_12: ZMKJABSEYRP5 · pith_short_16: ZMKJABSEYRP5IRZ5 · pith_short_8: ZMKJABSE

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/ZMKJABSEYRP5IRZ52MVSH6K7S7 \
  | 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: cb14900644c45fd4473dd32b23f95f97c27305cc5c3521cdd5a794ba74568dea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe8219e12737b221dcdfdd951f6a99a8d5f812a7f176c384116fe8e247bd54a7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-05-20T16:42:41Z",
    "title_canon_sha256": "4c8c7ef5176c2e2faa8a77a4e23fbd249a820060f69e8efb99eda94761df4c70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.12161",
    "kind": "arxiv",
    "version": 1
  }
}