Pith Number

pith:4YQXNDAA

pith:2012:4YQXNDAACEZJ5PWFAHPT2F7P2Y

not attested not anchored not stored refs pending

Affine dual equivalence and k-Schur functions

Sami Assaf, Sara Billey

arxiv:1201.2128 v1 · 2012-01-10 · 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{4YQXNDAACEZJ5PWFAHPT2F7P2Y}

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	2026-07-05T00:45:31.362217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e621768c0011329ebec501df3d17efd63fa38b276e85913dfb5239b75e92c0bd

Aliases

arxiv: 1201.2128 · arxiv_version: 1201.2128v1 · doi: 10.48550/arxiv.1201.2128 · pith_short_12: 4YQXNDAACEZJ · pith_short_16: 4YQXNDAACEZJ5PWF · pith_short_8: 4YQXNDAA

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/4YQXNDAACEZJ5PWFAHPT2F7P2Y \
  | 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: e621768c0011329ebec501df3d17efd63fa38b276e85913dfb5239b75e92c0bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "032141360688dad00a8bb6f5ef666bbd2f7e295aecf9c65d61067fa90821719e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-10T17:54:53Z",
    "title_canon_sha256": "93cbfa733f627b440f688df954dae5e66fde4bd28be3ca68da96f6e911762b8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2128",
    "kind": "arxiv",
    "version": 1
  }
}