Pith Number

pith:46652P4H

pith:2012:46652P4HGRLH2LEYHBID2DCZ3K

not attested not anchored not stored refs pending

Observability Inequalities and Measurable Sets

C. Zhang, G. Wang, J. Apraiz, L. Escauriaza

arxiv:1202.4876 v5 · 2012-02-22 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{46652P4HGRLH2LEYHBID2DCZ3K}

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	2026-05-18T03:21:10.704063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7bddd3f8734567d2c9838503d0c59da93743ad4ac2698a2dc4fa84f69ee0b25

Aliases

arxiv: 1202.4876 · arxiv_version: 1202.4876v5 · doi: 10.48550/arxiv.1202.4876 · pith_short_12: 46652P4HGRLH · pith_short_16: 46652P4HGRLH2LEY · pith_short_8: 46652P4H

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/46652P4HGRLH2LEYHBID2DCZ3K \
  | 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: e7bddd3f8734567d2c9838503d0c59da93743ad4ac2698a2dc4fa84f69ee0b25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d6fd2ae6064ee294b3d357f002c77b453f92d53688575dabc40009833a7585f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-02-22T10:49:34Z",
    "title_canon_sha256": "4d13b8701497dcf40008c96363d7a69acc76c23b32a0a4042a0b32fd87deaf2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4876",
    "kind": "arxiv",
    "version": 5
  }
}