Pith Number

pith:3KBW64KK

pith:2016:3KBW64KKBY46WWT4SWTZXDBZIY

not attested not anchored not stored refs pending

The Ramanujan Property for Simplicial Complexes

Uriya A. First

arxiv:1605.02664 v3 · 2016-05-09 · math.CO · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KBW64KKBY46WWT4SWTZXDBZIY}

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	2026-05-18T01:11:22.430093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da836f714a0e39eb5a7c95a79b8c3946132a676e58c079aeb7da1f81d6c9af87

Aliases

arxiv: 1605.02664 · arxiv_version: 1605.02664v3 · doi: 10.48550/arxiv.1605.02664 · pith_short_12: 3KBW64KKBY46 · pith_short_16: 3KBW64KKBY46WWT4 · pith_short_8: 3KBW64KK

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/3KBW64KKBY46WWT4SWTZXDBZIY \
  | 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: da836f714a0e39eb5a7c95a79b8c3946132a676e58c079aeb7da1f81d6c9af87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "943a27da6fdc76e35ec5c10d0755d48878f4510f039954f349e246dd15fa8f04",
    "cross_cats_sorted": [
      "math.NT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-09T17:32:02Z",
    "title_canon_sha256": "d6deb1f8f81b0cb938a23c292cc02034d7302cbfbe25ad3a7c0a926f46846bb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.02664",
    "kind": "arxiv",
    "version": 3
  }
}