Pith Number

pith:NPJW7552

pith:2016:NPJW7552QDNHTJHKMIUACNKWWW

not attested not anchored not stored refs pending

Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids

Kazuo Murota

arxiv:1608.07021 v2 · 2016-08-25 · 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{NPJW7552QDNHTJHKMIUACNKWWW}

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	2026-05-18T00:46:39.998912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bd36ff7ba80da79a4ea6228013556b5a6977b0e14e92d97f679c242efad88a9

Aliases

arxiv: 1608.07021 · arxiv_version: 1608.07021v2 · doi: 10.48550/arxiv.1608.07021 · pith_short_12: NPJW7552QDNH · pith_short_16: NPJW7552QDNHTJHK · pith_short_8: NPJW7552

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/NPJW7552QDNHTJHKMIUACNKWWW \
  | 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: 6bd36ff7ba80da79a4ea6228013556b5a6977b0e14e92d97f679c242efad88a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56ff6a118ac431b9496619cc2f301f6bad0e32947a0b84500c378e77c409dfc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-25T06:03:43Z",
    "title_canon_sha256": "9bb0672ce3e60d025d528bb60a269317bff0174ce205556623dc45a48c8c4052"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07021",
    "kind": "arxiv",
    "version": 2
  }
}