Pith Number

pith:B4FDMTZ7

pith:2010:B4FDMTZ73K6MT6MYUQBGKBJL6C

not attested not anchored not stored refs pending

Tensor products and Minkowski sums of Mirkovic-Vilonen polytopes

Daisuke Sagaki, Satoshi Naito, Syu Kato

arxiv:1010.0777 v1 · 2010-10-05 · math.QA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4FDMTZ73K6MT6MYUQBGKBJL6C}

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	2026-05-18T04:39:50.919852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f0a364f3fdabcc9f998a40265052bf09b25e00c73aa0ea586fb9f0090d329bc

Aliases

arxiv: 1010.0777 · arxiv_version: 1010.0777v1 · doi: 10.48550/arxiv.1010.0777 · pith_short_12: B4FDMTZ73K6M · pith_short_16: B4FDMTZ73K6MT6MY · pith_short_8: B4FDMTZ7

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/B4FDMTZ73K6MT6MYUQBGKBJL6C \
  | 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: 0f0a364f3fdabcc9f998a40265052bf09b25e00c73aa0ea586fb9f0090d329bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa818dc3527d7390649db8e3a7753e9e3769ec909b5f32b9fc2c213780bd5142",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-10-05T06:42:54Z",
    "title_canon_sha256": "ed52b583b3055aaf68ff317defe45682f3468e4b2430742ab2a9ed3fa7c64e77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0777",
    "kind": "arxiv",
    "version": 1
  }
}