Pith Number

pith:CAWFACCT

pith:1999:CAWFACCTP3SDHOMJ4HSLK3Q3KD

not attested not anchored not stored refs pending

Transversal fluctuations for increasing subsequences on the plane

Kurt Johansson

arxiv:math/9910146 v1 · 1999-10-27 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CAWFACCTP3SDHOMJ4HSLK3Q3KD}

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	2026-07-04T14:41:21.275601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

102c5008537ee433b989e1e4b56e1b50dc2eac94e924eacd63fb15446d8b5e92

Aliases

arxiv: math/9910146 · arxiv_version: math/9910146v1 · doi: 10.48550/arxiv.math/9910146 · pith_short_12: CAWFACCTP3SD · pith_short_16: CAWFACCTP3SDHOMJ · pith_short_8: CAWFACCT

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/CAWFACCTP3SDHOMJ4HSLK3Q3KD \
  | 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: 102c5008537ee433b989e1e4b56e1b50dc2eac94e924eacd63fb15446d8b5e92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99555c86f53fc3ba75a7174069a91509d17a74a5a17cb6f4935fd05176cd6600",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-10-27T08:20:28Z",
    "title_canon_sha256": "c414c1056cefc152d4e7d4c67eac1b2369aaff5ad38679770e8519cd13161b34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9910146",
    "kind": "arxiv",
    "version": 1
  }
}