Pith Number

pith:BMR6H4IF

pith:2017:BMR6H4IF67LCJCKSHWANGUWV6J

not attested not anchored not stored refs pending

A Stronger Multiple Exchange Property for M$^{\natural}$-concave Functions

Kazuo Murota

arxiv:1706.09222 v1 · 2017-06-28 · 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{BMR6H4IF67LCJCKSHWANGUWV6J}

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	2026-05-18T00:41:19.366906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b23e3f105f7d62489523d80d352d5f25192c5d9d7712fb48ec3c42dffdaad19

Aliases

arxiv: 1706.09222 · arxiv_version: 1706.09222v1 · doi: 10.48550/arxiv.1706.09222 · pith_short_12: BMR6H4IF67LC · pith_short_16: BMR6H4IF67LCJCKS · pith_short_8: BMR6H4IF

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/BMR6H4IF67LCJCKSHWANGUWV6J \
  | 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: 0b23e3f105f7d62489523d80d352d5f25192c5d9d7712fb48ec3c42dffdaad19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0663b5fa75737d762d1f9920964dc9b7a648054012f7a3643200cd6bd38e10e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-06-28T11:35:43Z",
    "title_canon_sha256": "be431b88f2f622be0cf4d486721880bba847c2e18075fd11c761f1d76357a9c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09222",
    "kind": "arxiv",
    "version": 1
  }
}