Pith Number

pith:OF6VGPWJ

pith:2026:OF6VGPWJM7LRNXHRO3K7TQ5EC3

not attested not anchored not stored refs pending

A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs

Jiechen Zhang

arxiv:2605.23773 v1 · 2026-05-22 · 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{OF6VGPWJM7LRNXHRO3K7TQ5EC3}

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	2026-05-25T02:02:31.835084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

717d533ec967d716dcf176d5f9c3a416dbaf07a760ec0df037b7acd7f78ddca7

Aliases

arxiv: 2605.23773 · arxiv_version: 2605.23773v1 · doi: 10.48550/arxiv.2605.23773 · pith_short_12: OF6VGPWJM7LR · pith_short_16: OF6VGPWJM7LRNXHR · pith_short_8: OF6VGPWJ

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/OF6VGPWJM7LRNXHRO3K7TQ5EC3 \
  | 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: 717d533ec967d716dcf176d5f9c3a416dbaf07a760ec0df037b7acd7f78ddca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1ac837723bc1c54a918345d86cc235d52ba34e60fbe1516f29bfaa844197914",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-22T15:41:44Z",
    "title_canon_sha256": "826a45d808745c5ef60698c74e076f795c9659de4d7f15e613e26d7099f8a07d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23773",
    "kind": "arxiv",
    "version": 1
  }
}