Pith Number

pith:THR4KB72

pith:2017:THR4KB723GV5WQJTWT4T4HUVXP

not attested not anchored not stored refs pending

Local spectral expansion approach to high dimensional expanders part I: Descent of spectral gaps

Izhar Oppenheim

arxiv:1709.04431 v1 · 2017-09-13 · 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{THR4KB723GV5WQJTWT4T4HUVXP}

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	2026-05-18T00:35:14.373793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99e3c507fad9abdb4133b4f93e1e95bbfc1dd7e240ebded24960f12efff98d46

Aliases

arxiv: 1709.04431 · arxiv_version: 1709.04431v1 · doi: 10.48550/arxiv.1709.04431 · pith_short_12: THR4KB723GV5 · pith_short_16: THR4KB723GV5WQJT · pith_short_8: THR4KB72

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/THR4KB723GV5WQJTWT4T4HUVXP \
  | 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: 99e3c507fad9abdb4133b4f93e1e95bbfc1dd7e240ebded24960f12efff98d46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86c191c6b306f08c9ea2030c91e0056eb16841d09d5c218377564bd93dec075a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-09-13T17:23:18Z",
    "title_canon_sha256": "728049d4e076a52de38bef93e77d1c56dccea7e8c6328028b095d789f9a61498"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.04431",
    "kind": "arxiv",
    "version": 1
  }
}