Pith Number

pith:XO6UBUCZ

pith:2015:XO6UBUCZ5MLUMOTPFB2JAJMRTM

not attested not anchored not stored refs pending

Spectrally extremal vertices, strong cospectrality and state transfer

Gabriel Coutinho

arxiv:1501.04398 v1 · 2015-01-19 · math.CO · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XO6UBUCZ5MLUMOTPFB2JAJMRTM}

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	2026-05-18T00:15:31.334123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a

Aliases

arxiv: 1501.04398 · arxiv_version: 1501.04398v1 · doi: 10.48550/arxiv.1501.04398 · pith_short_12: XO6UBUCZ5MLU · pith_short_16: XO6UBUCZ5MLUMOTP · pith_short_8: XO6UBUCZ

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/XO6UBUCZ5MLUMOTPFB2JAJMRTM \
  | 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: bbbd40d059eb17463a6f28749025919b26408be67c394a7f20673f3fc53f762a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee19f7e27da2fbebf19bb113cc7db3ce0b74a4c3f8fd2f47dd76da8105a7da23",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-19T06:15:21Z",
    "title_canon_sha256": "c71c6e5c05cff938ebb99b1a405e711aa36a98e2c3f01a742dc6d8bf89a5d91b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04398",
    "kind": "arxiv",
    "version": 1
  }
}