Pith Number

pith:MM6OA5AW

pith:2015:MM6OA5AWH3RPVKXW7SG6SVRUNC

not attested not anchored not stored refs pending

Hirsch polytopes with exponentially long combinatorial segments

Francisco Santos, Jean-Philippe Labb\'e, Thibault Manneville

arxiv:1510.07678 v1 · 2015-10-26 · math.CO · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MM6OA5AWH3RPVKXW7SG6SVRUNC}

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	2026-05-18T00:33:32.713905Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

633ce074163ee2faaaf6fc8de9563468bfca0ca068ceb2e735eb6a43a3c98006

Aliases

arxiv: 1510.07678 · arxiv_version: 1510.07678v1 · doi: 10.48550/arxiv.1510.07678 · pith_short_12: MM6OA5AWH3RP · pith_short_16: MM6OA5AWH3RPVKXW · pith_short_8: MM6OA5AW

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/MM6OA5AWH3RPVKXW7SG6SVRUNC \
  | 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: 633ce074163ee2faaaf6fc8de9563468bfca0ca068ceb2e735eb6a43a3c98006

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e46aa7c34619c7b4e0bfa0ceb78eebcdcf53a7d330b01526d091da60e858bb20",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-26T20:55:06Z",
    "title_canon_sha256": "38da7e5f4bb77e6c5c1e089f70adcb083e8e20d04b0b22c33a356cb94bcbdbe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07678",
    "kind": "arxiv",
    "version": 1
  }
}