Pith Number

pith:NFDVKRA4

pith:2017:NFDVKRA4RIBZ7PYCAZTNBLNIAD

not attested not anchored not stored refs pending

A tableau formula of double Grothendieck polynomials for $321$-avoiding permutations

Tomoo Matsumura

arxiv:1711.00147 v1 · 2017-11-01 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFDVKRA4RIBZ7PYCAZTNBLNIAD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:31:35.074477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

694755441c8a039fbf020666d0ada800e7dc5117dbf99beca163edd51b0c3f7a

Aliases

arxiv: 1711.00147 · arxiv_version: 1711.00147v1 · doi: 10.48550/arxiv.1711.00147 · pith_short_12: NFDVKRA4RIBZ · pith_short_16: NFDVKRA4RIBZ7PYC · pith_short_8: NFDVKRA4

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/NFDVKRA4RIBZ7PYCAZTNBLNIAD \
  | 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: 694755441c8a039fbf020666d0ada800e7dc5117dbf99beca163edd51b0c3f7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d59df93dfb4c0daafe40de3b7ddfad8a40f2512f30ae00c14d2e6cd9499cbd8c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-11-01T00:07:57Z",
    "title_canon_sha256": "bc4211d102cc1e680ea55f7850e18bb792d7db8b9f353b453f0648182e4a1957"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.00147",
    "kind": "arxiv",
    "version": 1
  }
}