Pith Number

pith:LPOQI5N6

pith:2019:LPOQI5N6PCIFRD45OBOQCKNMGP

not attested not anchored not stored refs pending

On the Betti and Tachibana numbers of compact Einstein manifolds

Irina Tsyganok, Sergey Stepanov, Vladimir Rovenski

arxiv:1908.07340 v2 · 2019-08-20 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPOQI5N6PCIFRD45OBOQCKNMGP}

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	2026-07-05T00:07:52.860031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bdd0475be7890588f9d705d0129ac33c0f397e24f05551c8c78233359a11b3c

Aliases

arxiv: 1908.07340 · arxiv_version: 1908.07340v2 · doi: 10.48550/arxiv.1908.07340 · pith_short_12: LPOQI5N6PCIF · pith_short_16: LPOQI5N6PCIFRD45 · pith_short_8: LPOQI5N6

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/LPOQI5N6PCIFRD45OBOQCKNMGP \
  | 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: 5bdd0475be7890588f9d705d0129ac33c0f397e24f05551c8c78233359a11b3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77eafae8a7cfa4f1883e57a886825e946887ccb8592859ec9c63d3dab818f8d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-08-20T13:43:52Z",
    "title_canon_sha256": "ac32286b1f89384847f069f352248c8e1d734700f4993433534468137b687e8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07340",
    "kind": "arxiv",
    "version": 2
  }
}