Pith Number

pith:FG4RPMB4

pith:2026:FG4RPMB4OZA2LDUH4F5KTPHV4D

not attested not anchored not stored refs pending

The size of the spanning-tree spectrum of simple graphs

Vishesh Jain

arxiv:2605.25088 v1 · 2026-05-24 · 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{FG4RPMB4OZA2LDUH4F5KTPHV4D}

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	2026-05-26T02:03:39.356724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b917b03c7641a58e87e17aa9bcf5e0e022446314a8f22c3a60aa6d9b508d3b

Aliases

arxiv: 2605.25088 · arxiv_version: 2605.25088v1 · doi: 10.48550/arxiv.2605.25088 · pith_short_12: FG4RPMB4OZA2 · pith_short_16: FG4RPMB4OZA2LDUH · pith_short_8: FG4RPMB4

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/FG4RPMB4OZA2LDUH4F5KTPHV4D \
  | 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: 29b917b03c7641a58e87e17aa9bcf5e0e022446314a8f22c3a60aa6d9b508d3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56b3d7b2788d12958de6232a7bc84b459aa815547d3f6808a8792b570bacf0a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-24T14:05:26Z",
    "title_canon_sha256": "4ba50382622c3c301e404146c76505506af340249f08012a3814daab60f7ef1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25088",
    "kind": "arxiv",
    "version": 1
  }
}