Pith Number

pith:D6F44JOS

pith:2011:D6F44JOSPIDIXDORRPXA7QFYS5

not attested not anchored not stored refs pending

The brick polytope of a sorting network

Francisco Santos, Vincent Pilaud

arxiv:1103.2731 v2 · 2011-03-14 · 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{D6F44JOSPIDIXDORRPXA7QFYS5}

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	2026-05-18T03:08:47.948024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f8bce25d27a068b8dd18bee0fc0b8977bb5ae50e493f58d35fd318fc85d3f84

Aliases

arxiv: 1103.2731 · arxiv_version: 1103.2731v2 · doi: 10.48550/arxiv.1103.2731 · pith_short_12: D6F44JOSPIDI · pith_short_16: D6F44JOSPIDIXDOR · pith_short_8: D6F44JOS

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/D6F44JOSPIDIXDORRPXA7QFYS5 \
  | 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: 1f8bce25d27a068b8dd18bee0fc0b8977bb5ae50e493f58d35fd318fc85d3f84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c3e837fb45d211314325f167498987bd3ead130cdeefaa9d8e557a299b120e8",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-14T18:22:11Z",
    "title_canon_sha256": "d968f364620b4a294d2dfe5977a2f86a84bd9a7c78ed72c14a5d8280cee83fe1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2731",
    "kind": "arxiv",
    "version": 2
  }
}