Pith Number

pith:2MI57YXW

pith:2015:2MI57YXWHBYCQ3PV44S77DP6PX

not attested not anchored not stored refs pending

Cluster duality and mirror symmetry for Grassmannians

Konstanze Rietsch, Lauren Williams

arxiv:1507.07817 v3 · 2015-07-28 · math.AG · math.CO · 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{2MI57YXWHBYCQ3PV44S77DP6PX}

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	2026-05-18T00:28:57.214797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d311dfe2f63870286df5e725ff8dfe7dd18b6950a719c207a6632629b079399f

Aliases

arxiv: 1507.07817 · arxiv_version: 1507.07817v3 · doi: 10.48550/arxiv.1507.07817 · pith_short_12: 2MI57YXWHBYC · pith_short_16: 2MI57YXWHBYCQ3PV · pith_short_8: 2MI57YXW

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/2MI57YXWHBYCQ3PV44S77DP6PX \
  | 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: d311dfe2f63870286df5e725ff8dfe7dd18b6950a719c207a6632629b079399f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "841518f3dddbbcc7c55b48fc9b4dfaaae54991f47c79a404f5c17f91ca921519",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-07-28T15:37:24Z",
    "title_canon_sha256": "8893a817164e9437a63ef8c3e45a8d7e4a00be3a4dff93681f8d8984dfcf37f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07817",
    "kind": "arxiv",
    "version": 3
  }
}