Pith Number

pith:QQRTA5NB

pith:2015:QQRTA5NBQLKB76SXO2HXOFP3AV

not attested not anchored not stored refs pending

Lower bound for the number of critical points of minimal spectral k-partitions for k large

Bernard Helffer

arxiv:1504.01015 v1 · 2015-04-04 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQRTA5NBQLKB76SXO2HXOFP3AV}

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	2026-05-18T02:19:35.364654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84233075a182d41ffa57768f7715fb0577b27cf7cc8df735adbfdc6b770380c0

Aliases

arxiv: 1504.01015 · arxiv_version: 1504.01015v1 · doi: 10.48550/arxiv.1504.01015 · pith_short_12: QQRTA5NBQLKB · pith_short_16: QQRTA5NBQLKB76SX · pith_short_8: QQRTA5NB

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/QQRTA5NBQLKB76SXO2HXOFP3AV \
  | 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: 84233075a182d41ffa57768f7715fb0577b27cf7cc8df735adbfdc6b770380c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "481d88d5e6c5a36298885874db1d0bb2a25aad92ed4d8431ba48b7300366d477",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-04T15:15:22Z",
    "title_canon_sha256": "e3b9ce5e3fa20a73a38e84da755567bc8bb857e7a08cbcba676c1564ecef857e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01015",
    "kind": "arxiv",
    "version": 1
  }
}