Pith Number

pith:JIMR4YNS

pith:2022:JIMR4YNSJ5YXLAMEVX4ZWMUIJV

not attested not anchored not stored refs pending

Bijective proofs of some coinversion identities related to Macdonald polynomials

Nicholas A. Loehr

arxiv:2210.11286 v1 · 2022-10-20 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JIMR4YNSJ5YXLAMEVX4ZWMUIJV}

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	2026-07-05T05:08:46.584165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a191e61b24f71758184adf99b32884d53b6b071288635836ca57b93a6b316ff

Aliases

arxiv: 2210.11286 · arxiv_version: 2210.11286v1 · doi: 10.48550/arxiv.2210.11286 · pith_short_12: JIMR4YNSJ5YX · pith_short_16: JIMR4YNSJ5YXLAME · pith_short_8: JIMR4YNS

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/JIMR4YNSJ5YXLAMEVX4ZWMUIJV \
  | 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: 4a191e61b24f71758184adf99b32884d53b6b071288635836ca57b93a6b316ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "229551312274b45049f08601b0d0edaee45d7f47bb119b880ae341959fbce758",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-10-20T14:06:46Z",
    "title_canon_sha256": "20992ce870db3e5b3705a1e7780bd3cd0e634d09ebc00a302397834cd337a3ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.11286",
    "kind": "arxiv",
    "version": 1
  }
}