Pith Number

pith:3JUTV2UH

pith:2021:3JUTV2UHFGJOCUTKBDTN4MLNZE

not attested not anchored not stored refs pending

Diameter estimates for graph associahedra

Jean Cardinal, Lionel Pournin, Mario Valencia-Pabon

arxiv:2106.16130 v2 · 2021-06-30 · 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{3JUTV2UHFGJOCUTKBDTN4MLNZE}

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	2026-07-05T05:20:07.978413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da693aea872992e1526a08e6de316dc92353d885ac6765b75969a4360f10171b

Aliases

arxiv: 2106.16130 · arxiv_version: 2106.16130v2 · doi: 10.48550/arxiv.2106.16130 · pith_short_12: 3JUTV2UHFGJO · pith_short_16: 3JUTV2UHFGJOCUTK · pith_short_8: 3JUTV2UH

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/3JUTV2UHFGJOCUTKBDTN4MLNZE \
  | 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: da693aea872992e1526a08e6de316dc92353d885ac6765b75969a4360f10171b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71d7f24067eee7ce233e3e4a16022659ecd94c077dd77dcdecaca98fdc92288c",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-06-30T15:32:12Z",
    "title_canon_sha256": "a2e15cd51a27b5b9cd76d60fdb7fca91f3325de6961277dc8a25eefd63bc42e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.16130",
    "kind": "arxiv",
    "version": 2
  }
}