Pith Number

pith:FXROPO7W

pith:2026:FXROPO7WBT3XG2AR4OWMATYJU6

not attested not anchored not stored refs pending

An Alexandrov-type theorem in warped product manifolds with radial density

Chao Xia, Jinchuan Bai

arxiv:2608.08548 v1 · 2026-08-09 · 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{FXROPO7WBT3XG2AR4OWMATYJU6}

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	2026-08-11T01:22:56.192019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2de2e7bbf60cf7736811e3acc04f09a793ccee96a9f1871e984d1f2a306a96a9

Aliases

arxiv: 2608.08548 · arxiv_version: 2608.08548v1 · doi: 10.48550/arxiv.2608.08548 · pith_short_12: FXROPO7WBT3X · pith_short_16: FXROPO7WBT3XG2AR · pith_short_8: FXROPO7W

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/FXROPO7WBT3XG2AR4OWMATYJU6 \
  | 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: 2de2e7bbf60cf7736811e3acc04f09a793ccee96a9f1871e984d1f2a306a96a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2dbe1efcdf356a4e51cf49a99af858d1a9c1afb1f884d8abb29fbcbadcd4342",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-08-09T07:47:26Z",
    "title_canon_sha256": "c93cbe8d2cf45f95261de493c37f5c14d550b1ee4a6e49f39886c46623892194"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08548",
    "kind": "arxiv",
    "version": 1
  }
}