Pith Number

pith:HLYYP4L5

pith:2016:HLYYP4L546WWJ5THAHMMZAEKEP

not attested not anchored not stored refs pending

Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra

Austin Stromme, Avi Levy, Collin Litterell, David Jekel, Will Dana

arxiv:1604.07075 v3 · 2016-04-24 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HLYYP4L546WWJ5THAHMMZAEKEP}

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	2026-05-18T00:15:10.763927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af187f17de7ad64f66701d8cc808a23f3dca7aab52fa584c198573c099a5064

Aliases

arxiv: 1604.07075 · arxiv_version: 1604.07075v3 · doi: 10.48550/arxiv.1604.07075 · pith_short_12: HLYYP4L546WW · pith_short_16: HLYYP4L546WWJ5TH · pith_short_8: HLYYP4L5

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/HLYYP4L546WWJ5THAHMMZAEKEP \
  | 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: 3af187f17de7ad64f66701d8cc808a23f3dca7aab52fa584c198573c099a5064

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fccc421042c7250b1706ea365e1c6429d378b6c6de30e5e2e6915e4f4aca1bc",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-24T19:27:24Z",
    "title_canon_sha256": "aaf4c5227755e246105cadf41edc8392b2b7208ccb60ed8f910992da1577a838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.07075",
    "kind": "arxiv",
    "version": 3
  }
}