Pith Number

pith:GHAPRZ5G

pith:2026:GHAPRZ5GL5B2DV7RQEVUB7UCZ2

not attested not anchored not stored refs pending

Think Through a Bottleneck: Hourglass Reasoning for Rigorous Induction

Huan Zhu

arxiv:2607.11696 v1 · 2026-07-13 · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHAPRZ5GL5B2DV7RQEVUB7UCZ2}

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	2026-07-14T02:22:19.460683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31c0f8e7a65f43a1d7f1812b40fe82ce93d77494d04b7920129c2e952f89f35a

Aliases

arxiv: 2607.11696 · arxiv_version: 2607.11696v1 · doi: 10.48550/arxiv.2607.11696 · pith_short_12: GHAPRZ5GL5B2 · pith_short_16: GHAPRZ5GL5B2DV7R · pith_short_8: GHAPRZ5G

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/GHAPRZ5GL5B2DV7RQEVUB7UCZ2 \
  | 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: 31c0f8e7a65f43a1d7f1812b40fe82ce93d77494d04b7920129c2e952f89f35a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59466446c3c382a8584b3120c6ec03480d31ceffc8db67d58798b24262ec75b7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-07-13T15:29:24Z",
    "title_canon_sha256": "c01df129cab0f110929c04491c69a5f26e2dfe0f6acbd07fb28d90b4a18bc13a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11696",
    "kind": "arxiv",
    "version": 1
  }
}