Pith Number

pith:LIXDHUML

pith:2010:LIXDHUMLJPRVKKKB64CHTP3KYL

not attested not anchored not stored refs pending

Mirkovi\'c-Vilonen Polytopes and a quiver construction of crystal basis in type $A$

Yoshihisa Saito

arxiv:1010.0086 v6 · 2010-10-01 · math.RT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LIXDHUMLJPRVKKKB64CHTP3KYL}

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	2026-05-18T04:30:35.200655Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a2e33d18b4be3552941f70479bf6ac2c882eec6af9b27d9c8ad8c8d352898b4

Aliases

arxiv: 1010.0086 · arxiv_version: 1010.0086v6 · doi: 10.48550/arxiv.1010.0086 · pith_short_12: LIXDHUMLJPRV · pith_short_16: LIXDHUMLJPRVKKKB · pith_short_8: LIXDHUML

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/LIXDHUMLJPRVKKKB64CHTP3KYL \
  | 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: 5a2e33d18b4be3552941f70479bf6ac2c882eec6af9b27d9c8ad8c8d352898b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "854fd31de8dbe09c31f87fdd03af04859f8fad53226fd7b4808f5c869d056d08",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-10-01T07:13:17Z",
    "title_canon_sha256": "e756bba38a381c9dbf857bd665d6107979b54da42b41460649d6133992943605"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0086",
    "kind": "arxiv",
    "version": 6
  }
}