Pith Number

pith:6GQNTPNB

pith:2018:6GQNTPNBB47QK7WWNG2UJCVYPM

not attested not anchored not stored refs pending

Uniqueness in Harper's vertex-isoperimetric theorem

Eero Raty

arxiv:1806.11061 v2 · 2018-06-28 · 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{6GQNTPNBB47QK7WWNG2UJCVYPM}

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

MICONIC: The spatial relationship between star formation and the AGN in Centaurus A revealed by JWST/MIRI

Receipt and verification

First computed	2026-07-05T00:14:17.775469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1a0d9bda10f3f057ed669b5448ab87b2c45488eb670978fee3dbec7c3eb03d1

Aliases

arxiv: 1806.11061 · arxiv_version: 1806.11061v2 · doi: 10.48550/arxiv.1806.11061 · pith_short_12: 6GQNTPNBB47Q · pith_short_16: 6GQNTPNBB47QK7WW · pith_short_8: 6GQNTPNB

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/6GQNTPNBB47QK7WWNG2UJCVYPM \
  | 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: f1a0d9bda10f3f057ed669b5448ab87b2c45488eb670978fee3dbec7c3eb03d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e7671b65aafd82997f0e0e2df17d3c66d715bcc3a1f28c19461437859a5c588",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-28T16:20:02Z",
    "title_canon_sha256": "4a13907259f9146dcd5eccd6ade1efcf27bce9adede9fceb786aec317194559f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.11061",
    "kind": "arxiv",
    "version": 2
  }
}