Pith Number

pith:T6UKGRPK

pith:2015:T6UKGRPKW2XBWVTJDVM2GFCHVL

not attested not anchored not stored refs pending

Effective masses for Laplacians on periodic graphs

Evgeny Korotyaev, Natalia Saburova

arxiv:1502.02989 v2 · 2015-02-10 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T6UKGRPKW2XBWVTJDVM2GFCHVL}

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	2026-05-18T02:17:11.198559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fa8a345eab6ae1b56691d59a31447aad2b2496de0bf6a164b4030149c05b6b6

Aliases

arxiv: 1502.02989 · arxiv_version: 1502.02989v2 · doi: 10.48550/arxiv.1502.02989 · pith_short_12: T6UKGRPKW2XB · pith_short_16: T6UKGRPKW2XBWVTJ · pith_short_8: T6UKGRPK

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/T6UKGRPKW2XBWVTJDVM2GFCHVL \
  | 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: 9fa8a345eab6ae1b56691d59a31447aad2b2496de0bf6a164b4030149c05b6b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80cdbe7184ced95599b93fe1627ae2ec23aea0df06e0ec975182ba8e0a949b3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-02-10T17:03:11Z",
    "title_canon_sha256": "18f67ed62b9ccd06b5215b83158da1c390e6408fa8057a6d72fee635776ccac0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02989",
    "kind": "arxiv",
    "version": 2
  }
}