Pith Number

pith:MEH4LVVJ

pith:2015:MEH4LVVJSEBXOPQWQYBYI6CLWZ

not attested not anchored not stored refs pending

Unstable CMC spheres and outlying CMC spheres in AF 3-manifolds

Shiguang Ma

arxiv:1507.02767 v3 · 2015-07-10 · 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{MEH4LVVJSEBXOPQWQYBYI6CLWZ}

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	2026-05-18T01:06:24.646715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

610fc5d6a99103773e16860384784bb659f91c15bdedd9cf0a0afcc55b853dfe

Aliases

arxiv: 1507.02767 · arxiv_version: 1507.02767v3 · doi: 10.48550/arxiv.1507.02767 · pith_short_12: MEH4LVVJSEBX · pith_short_16: MEH4LVVJSEBXOPQW · pith_short_8: MEH4LVVJ

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/MEH4LVVJSEBXOPQWQYBYI6CLWZ \
  | 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: 610fc5d6a99103773e16860384784bb659f91c15bdedd9cf0a0afcc55b853dfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cce362aa5b4b32c80b171e708d61e477d6ebe260d3387c9fc220de2f915007d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-07-10T02:31:24Z",
    "title_canon_sha256": "672276bf42611f82c57e7f35fa409cad78fdfbdc9fa2ba0079efa898738cb75f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02767",
    "kind": "arxiv",
    "version": 3
  }
}