Pith Number

pith:LUTTTK77

pith:2013:LUTTTK77ZDEYEDV7FGJP2LVS7Q

not attested not anchored not stored refs pending

Critical groups of covering, voltage, and signed graphs

Dennis Tseng, Victor Reiner

arxiv:1301.2977 v3 · 2013-01-14 · 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{LUTTTK77ZDEYEDV7FGJP2LVS7Q}

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	2026-07-05T01:08:19.826306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d2739abffc8c9820ebf2992fd2eb2fc038df432f5a78ff73c2fbf1a92a4a3fc

Aliases

arxiv: 1301.2977 · arxiv_version: 1301.2977v3 · doi: 10.48550/arxiv.1301.2977 · pith_short_12: LUTTTK77ZDEY · pith_short_16: LUTTTK77ZDEYEDV7 · pith_short_8: LUTTTK77

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/LUTTTK77ZDEYEDV7FGJP2LVS7Q \
  | 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: 5d2739abffc8c9820ebf2992fd2eb2fc038df432f5a78ff73c2fbf1a92a4a3fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb879d8716292276e6815aaa5eb2a91c398dfd0874affcc90a5a9218704fad89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-14T14:04:22Z",
    "title_canon_sha256": "128568ca615a9b3e783b47f7fe4ae9632cb39d00a6c169930e0b5512019f3963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2977",
    "kind": "arxiv",
    "version": 3
  }
}