Pith Number

pith:Y5PYV4HA

pith:2014:Y5PYV4HAKCON5I22IRBB2LR3I4

not attested not anchored not stored refs pending

A simple arithmetic criterion for graphs being determined by their generalized spectra

Wei Wang

arxiv:1410.2164 v3 · 2014-10-08 · 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{Y5PYV4HAKCON5I22IRBB2LR3I4}

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	2026-05-18T02:39:39.969677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29

Aliases

arxiv: 1410.2164 · arxiv_version: 1410.2164v3 · doi: 10.48550/arxiv.1410.2164 · pith_short_12: Y5PYV4HAKCON · pith_short_16: Y5PYV4HAKCON5I22 · pith_short_8: Y5PYV4HA

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/Y5PYV4HAKCON5I22IRBB2LR3I4 \
  | 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: c75f8af0e0509cdea35a44421d2e3b4719c15e45f2ccc81eb76b8d0abe6def29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ba506c0c6084b49d7b1fcbc69de1ade948dcc75c6e086809a9ede5e21cbc2bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-10-08T15:28:09Z",
    "title_canon_sha256": "5664562ac9b5cca8b57fae17488cb0880aa38a464cae68cee2fb4d33c025e05f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.2164",
    "kind": "arxiv",
    "version": 3
  }
}