Pith Number

pith:QQWMI33Y

pith:2015:QQWMI33Y2SP7TPEL5YXDKST7T5

not attested not anchored not stored refs pending

On the border lines between the regions of distinct solution type for solutions of the Friedmann equation satisfying the Hubble condition

Hellmut Baumg\"artel

arxiv:1511.02620 v3 · 2015-11-09 · 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{QQWMI33Y2SP7TPEL5YXDKST7T5}

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	2026-05-18T00:45:35.174027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

842cc46f78d49ff9bc8bee2e354a7f9f727147520e2760e5bebdd304808bc826

Aliases

arxiv: 1511.02620 · arxiv_version: 1511.02620v3 · doi: 10.48550/arxiv.1511.02620 · pith_short_12: QQWMI33Y2SP7 · pith_short_16: QQWMI33Y2SP7TPEL · pith_short_8: QQWMI33Y

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/QQWMI33Y2SP7TPEL5YXDKST7T5 \
  | 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: 842cc46f78d49ff9bc8bee2e354a7f9f727147520e2760e5bebdd304808bc826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ba5ec132bd2031e4eb0087ac1f23aec9b4cc84aa5e34e65c7f2045e1997e3ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-11-09T10:21:41Z",
    "title_canon_sha256": "c69607a3c846e59cb1e51b7a3f8880dd3afc36190b02ae55b139a2cbe958941a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02620",
    "kind": "arxiv",
    "version": 3
  }
}