Pith Number

pith:3RKGNB5Q

pith:2015:3RKGNB5QH2PGCOH3H5PMPLE757

not attested not anchored not stored refs pending

On the defect and stability of differential expansion

A. Morozov, Ya. Kononov

arxiv:1504.07146 v3 · 2015-04-27 · hep-th · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3RKGNB5QH2PGCOH3H5PMPLE757}

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	2026-05-18T01:34:12.871197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc546687b03e9e6138fb3f5ec7ac9fefe6250b6df66f5d0802ee73baa38ebbd9

Aliases

arxiv: 1504.07146 · arxiv_version: 1504.07146v3 · doi: 10.48550/arxiv.1504.07146 · pith_short_12: 3RKGNB5QH2PG · pith_short_16: 3RKGNB5QH2PGCOH3 · pith_short_8: 3RKGNB5Q

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/3RKGNB5QH2PGCOH3H5PMPLE757 \
  | 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: dc546687b03e9e6138fb3f5ec7ac9fefe6250b6df66f5d0802ee73baa38ebbd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5142aea011eb1a2a760ae473c0132f70a160744cbb6c6fc17a64fffc7ebcbc98",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2015-04-27T16:18:25Z",
    "title_canon_sha256": "b89459995b9048639abf382c9bf6aa6d836539325335b0b11cdd94445f6a426a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07146",
    "kind": "arxiv",
    "version": 3
  }
}