Pith Number

pith:5XF2UTIY

pith:2010:5XF2UTIYQOZZ5Y55KD3PT3WV37

not attested not anchored not stored refs pending

Packing spanning trees and the $k$-tree protocol

Brett Stevens, Robert F. Bailey

arxiv:1012.2478 v2 · 2010-12-11 · 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{5XF2UTIYQOZZ5Y55KD3PT3WV37}

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	2026-05-18T04:00:49.582998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edcbaa4d1883b39ee3bd50f6f9eed5dff80a41eeec468e9ccb05a1b61bc6ad56

Aliases

arxiv: 1012.2478 · arxiv_version: 1012.2478v2 · doi: 10.48550/arxiv.1012.2478 · pith_short_12: 5XF2UTIYQOZZ · pith_short_16: 5XF2UTIYQOZZ5Y55 · pith_short_8: 5XF2UTIY

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/5XF2UTIYQOZZ5Y55KD3PT3WV37 \
  | 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: edcbaa4d1883b39ee3bd50f6f9eed5dff80a41eeec468e9ccb05a1b61bc6ad56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "514f133fddce9cb1f63c2309065178efe12670b8e7908504d4cd0e8dc2f571c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-11T18:48:34Z",
    "title_canon_sha256": "0d71023ac9eb4e80b9c23474bae360c812be441efe68217976327c7863d416b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2478",
    "kind": "arxiv",
    "version": 2
  }
}