Pith Number

pith:5JE4DG2W

pith:2016:5JE4DG2WEOH4773LT6QY5WZQTQ

not attested not anchored not stored refs pending

The ABC's of affine Grassmannians and Hall-Littlewood polynomials

Avinash J. Dalal, Jennifer Morse

arxiv:1605.05405 v1 · 2016-05-18 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5JE4DG2WEOH4773LT6QY5WZQTQ}

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	2026-05-18T01:14:35.079791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea49c19b56238fcfff6b9fa18edb309c386bbcfae0cccf0b318c41129585fe72

Aliases

arxiv: 1605.05405 · arxiv_version: 1605.05405v1 · doi: 10.48550/arxiv.1605.05405 · pith_short_12: 5JE4DG2WEOH4 · pith_short_16: 5JE4DG2WEOH4773L · pith_short_8: 5JE4DG2W

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/5JE4DG2WEOH4773LT6QY5WZQTQ \
  | 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: ea49c19b56238fcfff6b9fa18edb309c386bbcfae0cccf0b318c41129585fe72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fbc597e3750595625433311aebe8c9961132124b3d8a0b56fb07dbe0ae2e63a",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-18T00:21:09Z",
    "title_canon_sha256": "ac9441dc7cb22c794eea2dfd42e20167c946218e2aa447239fb38824569e431e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05405",
    "kind": "arxiv",
    "version": 1
  }
}