Pith Number

pith:Q47ZG6HB

pith:2017:Q47ZG6HB6RFREDMPLEOBIBNEXP

not attested not anchored not stored refs pending

$A_{\alpha}$-spectrum of a graph obtained by copies of a rooted graph and applications

Oscar Rojo

arxiv:1704.06730 v1 · 2017-04-22 · 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{Q47ZG6HB6RFREDMPLEOBIBNEXP}

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	2026-05-18T00:45:57.751487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

873f9378e1f44b120d8f591c1405a4bbc875c6ce24b34562bf9af7b4232bf36e

Aliases

arxiv: 1704.06730 · arxiv_version: 1704.06730v1 · doi: 10.48550/arxiv.1704.06730 · pith_short_12: Q47ZG6HB6RFR · pith_short_16: Q47ZG6HB6RFREDMP · pith_short_8: Q47ZG6HB

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/Q47ZG6HB6RFREDMPLEOBIBNEXP \
  | 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: 873f9378e1f44b120d8f591c1405a4bbc875c6ce24b34562bf9af7b4232bf36e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11102e813a8a417fbd7cfde6cd412a3bb0a74262d6edbd9cf2ecdd4c02541708",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-04-22T01:07:01Z",
    "title_canon_sha256": "3b40bda872813283ee163e3b69591ae3839f769f3ad346bb70d6719b18c39ee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.06730",
    "kind": "arxiv",
    "version": 1
  }
}