Pith Number

pith:7F7SR3DN

pith:2011:7F7SR3DNKVZRPV64YNCZILLXWG

not attested not anchored not stored refs pending

Bounds of a number of leaves of spanning trees

Anton Bankevich, Dmitri Karpov

arxiv:1111.3266 v2 · 2011-11-14 · 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{7F7SR3DNKVZRPV64YNCZILLXWG}

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	2026-05-18T02:50:59.783158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f97f28ec6d557317d7dcc345942d77b19524e043a5950a4cf032144a813ae914

Aliases

arxiv: 1111.3266 · arxiv_version: 1111.3266v2 · doi: 10.48550/arxiv.1111.3266 · pith_short_12: 7F7SR3DNKVZR · pith_short_16: 7F7SR3DNKVZRPV64 · pith_short_8: 7F7SR3DN

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/7F7SR3DNKVZRPV64YNCZILLXWG \
  | 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: f97f28ec6d557317d7dcc345942d77b19524e043a5950a4cf032144a813ae914

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a5c8ccf0f95d4024ec47220c8cb450c06c63f04c7ff5ee62f8dadb46a5a7f6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-14T16:19:56Z",
    "title_canon_sha256": "8ba2e2e4d4fb8e03eeb072866a47eec628a57fc782f4d9a3d7806642f33bb6d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3266",
    "kind": "arxiv",
    "version": 2
  }
}