Pith Number

pith:CIKA3LDM

pith:2015:CIKA3LDM2OUOUL6DRF7HN4DYAZ

not attested not anchored not stored refs pending

From the weak Bruhat order to crystal posets

Cristian Lenart, Patricia Hersh

arxiv:1510.05636 v3 · 2015-10-19 · 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{CIKA3LDM2OUOUL6DRF7HN4DYAZ}

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	2026-05-18T01:02:04.844732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12140dac6cd3a8ea2fc3897e76f078066f5f0b2fb736ab28f12f722fa0260bf5

Aliases

arxiv: 1510.05636 · arxiv_version: 1510.05636v3 · doi: 10.48550/arxiv.1510.05636 · pith_short_12: CIKA3LDM2OUO · pith_short_16: CIKA3LDM2OUOUL6D · pith_short_8: CIKA3LDM

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/CIKA3LDM2OUOUL6DRF7HN4DYAZ \
  | 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: 12140dac6cd3a8ea2fc3897e76f078066f5f0b2fb736ab28f12f722fa0260bf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f532bcfee91da857f51c6605b4864a6e25e845d3a7c32902c2a86dfa7afcb83",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-19T19:54:43Z",
    "title_canon_sha256": "c8b68062964e1a1920dea116a3183ba3c9db23b6a6f56d8636b327ec6b66cbb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05636",
    "kind": "arxiv",
    "version": 3
  }
}