Pith Number

pith:VKXSUBSJ

pith:1999:VKXSUBSJSJROQFYIM344MOXG5A

not attested not anchored not stored refs pending

Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

Walter D. Neumann

arxiv:math/9901085 v2 · 1999-01-21 · 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{VKXSUBSJSJROQFYIM344MOXG5A}

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	2026-05-18T02:41:26.505943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaaf2a06499262e8170866f9c63ae6e80600175d29f2e2bbe4f6d75417fe2bc2

Aliases

arxiv: math/9901085 · arxiv_version: math/9901085v2 · doi: 10.48550/arxiv.math/9901085 · pith_short_12: VKXSUBSJSJRO · pith_short_16: VKXSUBSJSJROQFYI · pith_short_8: VKXSUBSJ

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/VKXSUBSJSJROQFYIM344MOXG5A \
  | 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: aaaf2a06499262e8170866f9c63ae6e80600175d29f2e2bbe4f6d75417fe2bc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d68aff498c6c984a6d0808bbb2697ceb6f438af79b09c8b6c544d577dab0e6c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-01-21T02:20:56Z",
    "title_canon_sha256": "a14fbb3c2d0da3d3cc5ab3c2b4689583775ca7873837c7265095565e3cd6d046"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9901085",
    "kind": "arxiv",
    "version": 2
  }
}