Pith Number

pith:Z3XGXP7K

pith:2020:Z3XGXP7KKKU2LJW6MUVHOWBMR3

not attested not anchored not stored refs pending

Reeb spaces of smooth functions on manifolds

Osamu Saeki

arxiv:2006.01689 v1 · 2020-06-02 · 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{Z3XGXP7KKKU2LJW6MUVHOWBMR3}

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.

Cited by

1 paper in Pith

Compactifying real analytic functions and resulting Reeb spaces

Receipt and verification

First computed	2026-07-05T01:07:33.267349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceee6bbfea52a9a5a6de652a77582c8ee897400694ebdd1dd0f37ca9c8dcec6b

Aliases

arxiv: 2006.01689 · arxiv_version: 2006.01689v1 · doi: 10.48550/arxiv.2006.01689 · pith_short_12: Z3XGXP7KKKU2 · pith_short_16: Z3XGXP7KKKU2LJW6 · pith_short_8: Z3XGXP7K

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/Z3XGXP7KKKU2LJW6MUVHOWBMR3 \
  | 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: ceee6bbfea52a9a5a6de652a77582c8ee897400694ebdd1dd0f37ca9c8dcec6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db53cb5b652628acdb386642995c8580ef2d19f9f12db0af6ec1a6f7dab5f4dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-06-02T15:04:35Z",
    "title_canon_sha256": "7912dfcc9cb745f99c265e56c8c6e3b1b3384ce377ada27944534a090983cebc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.01689",
    "kind": "arxiv",
    "version": 1
  }
}