Pith Number

pith:G4ULR4AX

pith:2017:G4ULR4AXMPX6QUJD6QOSI4VIMZ

not attested not anchored not stored refs pending

A trinity of duality: non-separable planar maps, $\beta$-(1,0) trees and synchronized intervals

Wenjie Fang

arxiv:1703.02774 v2 · 2017-03-08 · 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{G4ULR4AXMPX6QUJD6QOSI4VIMZ}

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	2026-05-18T00:30:30.582668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3728b8f01763efe85123f41d2472a866620913a4778d520bd9e360b1c63ecc31

Aliases

arxiv: 1703.02774 · arxiv_version: 1703.02774v2 · doi: 10.48550/arxiv.1703.02774 · pith_short_12: G4ULR4AXMPX6 · pith_short_16: G4ULR4AXMPX6QUJD · pith_short_8: G4ULR4AX

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/G4ULR4AXMPX6QUJD6QOSI4VIMZ \
  | 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: 3728b8f01763efe85123f41d2472a866620913a4778d520bd9e360b1c63ecc31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0eae44bd81c18e66b239cee33209e723e73bb1749c2f48732ef6913422086a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-03-08T10:20:56Z",
    "title_canon_sha256": "e9df9aa2efa5f252bc140f445443b57719eb3465210c27c0557078e387cb4b5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.02774",
    "kind": "arxiv",
    "version": 2
  }
}