Pith Number

pith:5SHY7ALG

pith:2026:5SHY7ALGNX7RCUICYYWC5KZ5O3

not attested not anchored not stored refs pending

Geometric obstruction to resolving the Hubble tension: orthogonality of scale and shape in distance measurements

Chaoqian Ai, Hongchao Zhang, Sheng Bi, Zhihuan Zhou, Zhuang Miao

arxiv:2606.12822 v1 · 2026-06-11 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5SHY7ALGNX7RCUICYYWC5KZ5O3}

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	2026-06-12T01:08:52.792351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec8f8f81666dff115102c62c2eab3d76d702fda0a6c96785c8b394a6ad388228

Aliases

arxiv: 2606.12822 · arxiv_version: 2606.12822v1 · doi: 10.48550/arxiv.2606.12822 · pith_short_12: 5SHY7ALGNX7R · pith_short_16: 5SHY7ALGNX7RCUIC · pith_short_8: 5SHY7ALG

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/5SHY7ALGNX7RCUICYYWC5KZ5O3 \
  | 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: ec8f8f81666dff115102c62c2eab3d76d702fda0a6c96785c8b394a6ad388228

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6803c5b61ad112da2050cc6d26527f75424b249170202c58fc899a11f8cc73a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-06-11T02:35:35Z",
    "title_canon_sha256": "0df97a9d2dc67b962251b448db078c98b266e67f945f1c3733a8d0c5d3e950d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12822",
    "kind": "arxiv",
    "version": 1
  }
}