Pith Number

pith:TGICCZWW

pith:2016:TGICCZWWHU5TY47TNUMFMDQA4T

not attested not anchored not stored refs pending

On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

Matthias K\"oppe, Yuan Zhou

arxiv:1611.06626 v1 · 2016-11-21 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TGICCZWWHU5TY47TNUMFMDQA4T}

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	2026-05-18T00:40:28.705772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99902166d63d3b3c73f36d18560e00e4e10b3750bc1a201d98a83a74150242f8

Aliases

arxiv: 1611.06626 · arxiv_version: 1611.06626v1 · doi: 10.48550/arxiv.1611.06626 · pith_short_12: TGICCZWWHU5T · pith_short_16: TGICCZWWHU5TY47T · pith_short_8: TGICCZWW

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/TGICCZWWHU5TY47TNUMFMDQA4T \
  | 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: 99902166d63d3b3c73f36d18560e00e4e10b3750bc1a201d98a83a74150242f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c94d7a24fd06cf97c0f8cf6f986846f9fb48a8d62a0a0c3bf679e03f5a8bec97",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-11-21T01:13:58Z",
    "title_canon_sha256": "3b399f6fc2d19d54e0883bfe7b90e66731ef15d51d9c0b77508b13b9ec460d10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06626",
    "kind": "arxiv",
    "version": 1
  }
}