Pith Number

pith:6VM5L5YL

pith:2016:6VM5L5YLGHOHDWE7XRCM2YFPAY

not attested not anchored not stored refs pending

Homomorphisms into loop-threshold graphs

Jonathan Cutler, Nicholas Kass

arxiv:1606.02660 v1 · 2016-06-08 · 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{6VM5L5YLGHOHDWE7XRCM2YFPAY}

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	2026-05-18T01:12:40.890177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f559d5f70b31dc71d89fbc44cd60af061a90c45b9e5dcd45cccd26fbdc43688d

Aliases

arxiv: 1606.02660 · arxiv_version: 1606.02660v1 · doi: 10.48550/arxiv.1606.02660 · pith_short_12: 6VM5L5YLGHOH · pith_short_16: 6VM5L5YLGHOHDWE7 · pith_short_8: 6VM5L5YL

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/6VM5L5YLGHOHDWE7XRCM2YFPAY \
  | 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: f559d5f70b31dc71d89fbc44cd60af061a90c45b9e5dcd45cccd26fbdc43688d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91c6a6acb759e9c01be9f6eaac000dc35150e3a72576155f8b252309474b7fd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-08T17:55:50Z",
    "title_canon_sha256": "2ad53b7d2cb104626db7adc16d3a50ed0ae79287e14a4d84ed8019d448d9eef2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.02660",
    "kind": "arxiv",
    "version": 1
  }
}