Pith Number

pith:23HDCAE5

pith:2011:23HDCAE5CH2E4TXMRYIPBEPTMV

not attested not anchored not stored refs pending

The down operator and expansions of near rectangular k-Schur functions

Chris Berg, Franco Saliola, Luis Serrano

arxiv:1112.4460 v3 · 2011-12-19 · 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{23HDCAE5CH2E4TXMRYIPBEPTMV}

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	2026-05-18T04:02:03.665657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6ce31009d11f44e4eec8e10f091f3657c5885757a75daf91554bdc7e3b1af0b

Aliases

arxiv: 1112.4460 · arxiv_version: 1112.4460v3 · doi: 10.48550/arxiv.1112.4460 · pith_short_12: 23HDCAE5CH2E · pith_short_16: 23HDCAE5CH2E4TXM · pith_short_8: 23HDCAE5

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/23HDCAE5CH2E4TXMRYIPBEPTMV \
  | 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: d6ce31009d11f44e4eec8e10f091f3657c5885757a75daf91554bdc7e3b1af0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b18d14033fbf39a5c67891dd689c1d163f12708fe4d64f4f833312abba92ce60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-19T20:42:53Z",
    "title_canon_sha256": "65f6c1eaddacb58ed4691e6aaab51aa4fc5d2635d2a5a214414ca864d42a6301"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4460",
    "kind": "arxiv",
    "version": 3
  }
}