Pith Number

pith:BRK4XG6A

pith:2026:BRK4XG6ALZDA35ZWAO4Y4Y6XUX

not attested not anchored not stored refs pending

Supermodularity and Submodularity in Network Interdiction

Bo Zhou, Ruiwei Jiang, Siqian Shen

arxiv:2606.10345 v1 · 2026-06-09 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRK4XG6ALZDA35ZWAO4Y4Y6XUX}

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	2026-06-10T01:10:12.853022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c55cb9bc05e460df73603b98e63d7a5d6c71f5e830d319a59b92cf59a0f4d2f

Aliases

arxiv: 2606.10345 · arxiv_version: 2606.10345v1 · doi: 10.48550/arxiv.2606.10345 · pith_short_12: BRK4XG6ALZDA · pith_short_16: BRK4XG6ALZDA35ZW · pith_short_8: BRK4XG6A

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/BRK4XG6ALZDA35ZWAO4Y4Y6XUX \
  | 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: 0c55cb9bc05e460df73603b98e63d7a5d6c71f5e830d319a59b92cf59a0f4d2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94ffa86c333d10c1179cb2c88108aaf2ed843a6e00e5273e139beeea7ae653fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-09T02:54:27Z",
    "title_canon_sha256": "475e8d5dbec10322bb15c9585662d780d823649d9224aa73f316da6db6d33238"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10345",
    "kind": "arxiv",
    "version": 1
  }
}