Pith Number

pith:FLJT7H7O

pith:2015:FLJT7H7OKA4LLPOWBPL2I2SPLJ

not attested not anchored not stored refs pending

Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes

Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava

arxiv:1505.08010 v1 · 2015-05-29 · 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{FLJT7H7OKA4LLPOWBPL2I2SPLJ}

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	2026-05-18T02:00:00.051685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ad33f9fee5038b5bdd60bd7a46a4f5a74552b7cb89a59759d57771a2ed57f38

Aliases

arxiv: 1505.08010 · arxiv_version: 1505.08010v1 · doi: 10.48550/arxiv.1505.08010 · pith_short_12: FLJT7H7OKA4L · pith_short_16: FLJT7H7OKA4LLPOW · pith_short_8: FLJT7H7O

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/FLJT7H7OKA4LLPOWBPL2I2SPLJ \
  | 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: 2ad33f9fee5038b5bdd60bd7a46a4f5a74552b7cb89a59759d57771a2ed57f38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fcd0d991100123bb7032b8448215d537f6949e575aa240897d9fafdc1edc987",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-29T12:13:38Z",
    "title_canon_sha256": "f39fc20b786beef98b75b15d892cb4b5ae8fee932f5c765701a194b7a2e4b4c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.08010",
    "kind": "arxiv",
    "version": 1
  }
}