Pith Number

pith:NIOAMRNE

pith:2021:NIOAMRNEECJPE2YF4XYL44RVQE

not attested not anchored not stored refs pending

A Koopman Operator Tutorial with Othogonal Polynomials

David Arnas, Richard Linares, Simone Servadio

arxiv:2111.07485 v2 · 2021-11-15 · math.NA · cs.NA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NIOAMRNEECJPE2YF4XYL44RVQE}

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	2026-07-05T04:40:08.138461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a1c0645a42092f26b05e5f0be723581291921d74125a339aba9de24056aa251

Aliases

arxiv: 2111.07485 · arxiv_version: 2111.07485v2 · doi: 10.48550/arxiv.2111.07485 · pith_short_12: NIOAMRNEECJP · pith_short_16: NIOAMRNEECJPE2YF · pith_short_8: NIOAMRNE

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/NIOAMRNEECJPE2YF4XYL44RVQE \
  | 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: 6a1c0645a42092f26b05e5f0be723581291921d74125a339aba9de24056aa251

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efa4c55875faea0c93d3662acfc821e27e80e667cfe44d4d1c294b58b26d068b",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2021-11-15T01:32:29Z",
    "title_canon_sha256": "511292c365273d788b008cb3bb34494e4fc86749ff224305b0d4a355a49632c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.07485",
    "kind": "arxiv",
    "version": 2
  }
}