Pith Number

pith:7BADSM6M

pith:2010:7BADSM6MWRYGUSOZII3QZYJX4P

not attested not anchored not stored refs pending

A Littlewood-Richardson rule for Macdonald polynomials

Martha Yip

arxiv:1010.0722 v1 · 2010-10-04 · 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{7BADSM6MWRYGUSOZII3QZYJX4P}

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	2026-05-18T04:39:50.973472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8403933ccb4706a49d942370ce137e3e7a8b1af183819a8d4ef92f7d51119bc

Aliases

arxiv: 1010.0722 · arxiv_version: 1010.0722v1 · doi: 10.48550/arxiv.1010.0722 · pith_short_12: 7BADSM6MWRYG · pith_short_16: 7BADSM6MWRYGUSOZ · pith_short_8: 7BADSM6M

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/7BADSM6MWRYGUSOZII3QZYJX4P \
  | 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: f8403933ccb4706a49d942370ce137e3e7a8b1af183819a8d4ef92f7d51119bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6d8d907460e31f8be083d8f3fa1665c3fa4f5eee7a84961275161c694815fce",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-04T22:32:56Z",
    "title_canon_sha256": "74d04bf050dc677aba444f28e735563077e303a63c484585bd54e12f65920b68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0722",
    "kind": "arxiv",
    "version": 1
  }
}