Pith Number

pith:PJZWIMC7

pith:2021:PJZWIMC7YXFDKN5MSGUHT7A6KV

not attested not anchored not stored refs pending

On Langmuir's periodic orbit

Kai Cieliebak, Martin Schwingenheuer, Urs Frauenfelder

arxiv:2108.13762 v3 · 2021-08-31 · math.SG · 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{PJZWIMC7YXFDKN5MSGUHT7A6KV}

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	2026-07-05T06:36:19.576737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a7364305fc5ca3537ac91a879fc1e55487bd741f98b2d38a96c8176612de23d

Aliases

arxiv: 2108.13762 · arxiv_version: 2108.13762v3 · doi: 10.48550/arxiv.2108.13762 · pith_short_12: PJZWIMC7YXFD · pith_short_16: PJZWIMC7YXFDKN5M · pith_short_8: PJZWIMC7

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/PJZWIMC7YXFDKN5MSGUHT7A6KV \
  | 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: 7a7364305fc5ca3537ac91a879fc1e55487bd741f98b2d38a96c8176612de23d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c2be2f6bdf885d8457a12782e8d7ff68f234204595bd8b98497131440aa1cdf",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2021-08-31T11:26:48Z",
    "title_canon_sha256": "cb1240835093c2279cc144d409c824b1864cec499922fe149331966849c99445"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.13762",
    "kind": "arxiv",
    "version": 3
  }
}