Pith Number

pith:ALKY5SVE

pith:2022:ALKY5SVEW6YWIKBHGFJ3OO3W3H

not attested not anchored not stored refs pending

Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions

Adam Cie\'slik, Patryk Mach

arxiv:2203.12401 v4 · 2022-03-23 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ALKY5SVEW6YWIKBHGFJ3OO3W3H}

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	2026-07-05T05:02:41.458369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02d58ecaa4b7b16428273153b73b76d9d232a4312fb2fd7a939393bbfcd8af4d

Aliases

arxiv: 2203.12401 · arxiv_version: 2203.12401v4 · doi: 10.48550/arxiv.2203.12401 · pith_short_12: ALKY5SVEW6YW · pith_short_16: ALKY5SVEW6YWIKBH · pith_short_8: ALKY5SVE

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/ALKY5SVEW6YWIKBHGFJ3OO3W3H \
  | 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: 02d58ecaa4b7b16428273153b73b76d9d232a4312fb2fd7a939393bbfcd8af4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58482de3d7ad7ccfa7cdd2108d32f0fc918c0aa83106fb2835eed5c195158fb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-03-23T13:23:31Z",
    "title_canon_sha256": "b70cf3e16399285d170f5c4ddcbd5f28a6bdac79713de771916921762a9f1a4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.12401",
    "kind": "arxiv",
    "version": 4
  }
}