Pith Number

pith:6R77W4AU

pith:2026:6R77W4AUTNJ2ODYWQBE56LYJS5

not attested not anchored not stored refs pending

Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams

Anna Weigandt, Laura Escobar, Patricia Klein

arxiv:2606.13518 v1 · 2026-06-11 · 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{6R77W4AUTNJ2ODYWQBE56LYJS5}

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	2026-06-12T01:10:07.973375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f47ffb70149b53a70f168049df2f09976e841b33511c52502d06ead1675560c8

Aliases

arxiv: 2606.13518 · arxiv_version: 2606.13518v1 · doi: 10.48550/arxiv.2606.13518 · pith_short_12: 6R77W4AUTNJ2 · pith_short_16: 6R77W4AUTNJ2ODYW · pith_short_8: 6R77W4AU

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/6R77W4AUTNJ2ODYWQBE56LYJS5 \
  | 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: f47ffb70149b53a70f168049df2f09976e841b33511c52502d06ead1675560c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e741b4c04438b25473399ca37999b386df7a037eb7fda45633f9bfb7f71dd6de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-11T16:09:05Z",
    "title_canon_sha256": "c888cc95277f638eda4ecf242ca54e56ba7564796104a358d5ff0c775bc86d4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13518",
    "kind": "arxiv",
    "version": 1
  }
}