Pith Number

pith:6TFCHSLP

pith:2026:6TFCHSLPTXVNCAR4F7IERKWKHT

not attested not anchored not stored refs pending

General Relativistic Shock Wave Solutions with Black Hole Formation: The Singular Isothermal Sphere Case

(2) Google, (3) CfA/SAO), Chien-Ting J. Chen (1), Fabio Pacucci (3) ((1) USRA/NASA MSFC, Michael J. Cai (2)

arxiv:2606.29607 v1 · 2026-06-28 · astro-ph.HE · astro-ph.CO · astro-ph.GA · 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{6TFCHSLPTXVNCAR4F7IERKWKHT}

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	2026-06-30T01:18:19.079558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4ca23c96f9dead1023c2fd048aaca3ce1a2c434c02efade20761df209384847

Aliases

arxiv: 2606.29607 · arxiv_version: 2606.29607v1 · doi: 10.48550/arxiv.2606.29607 · pith_short_12: 6TFCHSLPTXVN · pith_short_16: 6TFCHSLPTXVNCAR4 · pith_short_8: 6TFCHSLP

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/6TFCHSLPTXVNCAR4F7IERKWKHT \
  | 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: f4ca23c96f9dead1023c2fd048aaca3ce1a2c434c02efade20761df209384847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e68798fc0cb6746a0f98bdf68594aa365784a417389471d8b6a693489b7a349",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "astro-ph.GA",
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.HE",
    "submitted_at": "2026-06-28T21:18:59Z",
    "title_canon_sha256": "cd2e1a3590ab32d909b4c8666d68d9a67f1976723bb77d758b8097c60ea6f326"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29607",
    "kind": "arxiv",
    "version": 1
  }
}