Pith Number

pith:TXLMK5O6

pith:2013:TXLMK5O6QBYDTUAQQWNA5BA2XG

not attested not anchored not stored refs pending

Isometric immersions of higher codimension into the product ${\mathbf S^k \times H^{n+p-k}}$ of sphere and hyperboloid

Tianqun Zhang, Xingxiao Li

arxiv:1311.3849 v1 · 2013-11-15 · 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{TXLMK5O6QBYDTUAQQWNA5BA2XG}

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	2026-05-18T03:07:02.884041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd6c575de807039d010859a0e841ab9a85a6ae6f2760e11320967db8c9e9ef2

Aliases

arxiv: 1311.3849 · arxiv_version: 1311.3849v1 · doi: 10.48550/arxiv.1311.3849 · pith_short_12: TXLMK5O6QBYD · pith_short_16: TXLMK5O6QBYDTUAQ · pith_short_8: TXLMK5O6

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/TXLMK5O6QBYDTUAQQWNA5BA2XG \
  | 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: 9dd6c575de807039d010859a0e841ab9a85a6ae6f2760e11320967db8c9e9ef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80abd98252689a2abc8684bf5a410635f5b352c3994d014749e6948ecf5501c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-11-15T13:42:54Z",
    "title_canon_sha256": "53e6d876400ce37e140db5a46c7d6b38b6460db870cc145389bf38e3e65906b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3849",
    "kind": "arxiv",
    "version": 1
  }
}