Pith Number

pith:KPKEB4T2

pith:2016:KPKEB4T23UOTVWQVUMJ753FKKK

not attested not anchored not stored refs pending

Lp expander Complexes

Amitay Kamber

arxiv:1701.00154 v1 · 2016-12-31 · 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{KPKEB4T23UOTVWQVUMJ753FKKK}

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 Bigraphs

Receipt and verification

First computed	2026-05-18T00:53:36.224484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53d440f27add1d3ada15a313feecaa5293c03addee2558b60f6766cfb92b8506

Aliases

arxiv: 1701.00154 · arxiv_version: 1701.00154v1 · doi: 10.48550/arxiv.1701.00154 · pith_short_12: KPKEB4T23UOT · pith_short_16: KPKEB4T23UOTVWQV · pith_short_8: KPKEB4T2

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/KPKEB4T23UOTVWQVUMJ753FKKK \
  | 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: 53d440f27add1d3ada15a313feecaa5293c03addee2558b60f6766cfb92b8506

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6de638c3f7224706346020ac6a69c7035341ae0edf0da27e43676a751eb4604d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-31T18:26:16Z",
    "title_canon_sha256": "904086f2bf8b550b1aaa9d3a2fec726571b55a0e5759f80a5ca914fca7314829"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.00154",
    "kind": "arxiv",
    "version": 1
  }
}