Pith Number

pith:OP5Z4PNQ

pith:2025:OP5Z4PNQLRPUU5FGZJLASUCCI6

not attested not anchored not stored refs pending

IP Models for Minimum Zero Forcing Sets, Forts, and Related Graph Parameters

Jonad Pulaj, Thomas R. Cameron

arxiv:2508.07293 v1 · 2025-08-10 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OP5Z4PNQLRPUU5FGZJLASUCCI6}

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	2026-07-05T11:51:43.942936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73fb9e3db05c5f4a74a6ca56095042479988f5d67d194aba64b9b4f98e822610

Aliases

arxiv: 2508.07293 · arxiv_version: 2508.07293v1 · doi: 10.48550/arxiv.2508.07293 · pith_short_12: OP5Z4PNQLRPU · pith_short_16: OP5Z4PNQLRPUU5FG · pith_short_8: OP5Z4PNQ

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/OP5Z4PNQLRPUU5FGZJLASUCCI6 \
  | 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: 73fb9e3db05c5f4a74a6ca56095042479988f5d67d194aba64b9b4f98e822610

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "349523359e40104de808aff0724e577d19f7ba5a4e544974fa1c6855ed34f17e",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-10T11:05:27Z",
    "title_canon_sha256": "7bdd620c742e4960d7e8cd7e45b870a2a42fdb9edfd3fc15dbc17a64d73ba3ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.07293",
    "kind": "arxiv",
    "version": 1
  }
}