Pith Number

pith:JI5J6JR5

pith:2016:JI5J6JR5S7HSUGDKT27YHGTNHP

not attested not anchored not stored refs pending

Neumann Cheeger constants on graphs

Hua Bobo, Huang Yan

arxiv:1610.01360 v1 · 2016-10-05 · math.SP · 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{JI5J6JR5S7HSUGDKT27YHGTNHP}

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	2026-05-18T01:03:11.056083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a3a9f263d97cf2a186a9ebf839a6d3bd16a461896a1dd166ff59861f2a55c0b

Aliases

arxiv: 1610.01360 · arxiv_version: 1610.01360v1 · doi: 10.48550/arxiv.1610.01360 · pith_short_12: JI5J6JR5S7HS · pith_short_16: JI5J6JR5S7HSUGDK · pith_short_8: JI5J6JR5

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/JI5J6JR5S7HSUGDKT27YHGTNHP \
  | 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: 4a3a9f263d97cf2a186a9ebf839a6d3bd16a461896a1dd166ff59861f2a55c0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61ce2984d2fb8ba381a4091ab7530750f379cf81f02845a90d84ac1939df522e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-10-05T11:13:35Z",
    "title_canon_sha256": "7e407b49e465a4b2050d302605fb9d6af4cba0f7f1659ac06ecfdb4b7ed77ddd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01360",
    "kind": "arxiv",
    "version": 1
  }
}