Pith Number

pith:KNOE4D44

pith:2016:KNOE4D445LQJ4USYZSJNWBAPIU

not attested not anchored not stored refs pending

Comparing the Morse index and the first Betti number of minimal hypersurfaces

Alessandro Carlotto, Ben Sharp, Lucas Ambrozio

arxiv:1601.08152 v2 · 2016-01-29 · 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{KNOE4D445LQJ4USYZSJNWBAPIU}

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	2026-05-18T01:10:23.494079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535c4e0f9ceae09e5258cc92db040f453d3865f49d45ec8e7cace90a03e3ede8

Aliases

arxiv: 1601.08152 · arxiv_version: 1601.08152v2 · doi: 10.48550/arxiv.1601.08152 · pith_short_12: KNOE4D445LQJ · pith_short_16: KNOE4D445LQJ4USY · pith_short_8: KNOE4D44

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/KNOE4D445LQJ4USYZSJNWBAPIU \
  | 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: 535c4e0f9ceae09e5258cc92db040f453d3865f49d45ec8e7cace90a03e3ede8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a840df1a59c4a4fd6056440147896bc75300b5e6c0443c8d48eea79bde99246",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-01-29T15:26:57Z",
    "title_canon_sha256": "e4e910566dbe4b4509cb48f89cefbebd63788479dcf0b43011b7921e71d07d37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.08152",
    "kind": "arxiv",
    "version": 2
  }
}