Pith Number

pith:M3THJMTY

pith:2020:M3THJMTYU4FX5SGMHT7ZWEQSSM

not attested not anchored not stored refs pending

Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids

Natalie C. Behague, Pawel Pralat, Trent Marbach

arxiv:2012.00216 v2 · 2020-12-01 · 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{M3THJMTYU4FX5SGMHT7ZWEQSSM}

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	2026-07-05T02:23:20.022886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66e674b278a70b7ec8cc3cff9b1212932387788c548c85d12e5da95b1f87a527

Aliases

arxiv: 2012.00216 · arxiv_version: 2012.00216v2 · doi: 10.48550/arxiv.2012.00216 · pith_short_12: M3THJMTYU4FX · pith_short_16: M3THJMTYU4FX5SGM · pith_short_8: M3THJMTY

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/M3THJMTYU4FX5SGMHT7ZWEQSSM \
  | 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: 66e674b278a70b7ec8cc3cff9b1212932387788c548c85d12e5da95b1f87a527

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941488d14e10a5d458ea3bc6a3691ba6ec1c3e24afb8dbd008699c7fc183450f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-12-01T02:09:56Z",
    "title_canon_sha256": "cf6de043096979d0984e0dde0ff1a6690de213eb1a6a25e40494b83b9af25734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.00216",
    "kind": "arxiv",
    "version": 2
  }
}