Pith Number

pith:MVUNDVZJ

pith:2011:MVUNDVZJLK6PL4DSITNFI6NO6H

not attested not anchored not stored refs pending

Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families

Joshua M. Sabloff, Lisa Traynor

arxiv:1109.5660 v3 · 2011-09-26 · math.SG · 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{MVUNDVZJLK6PL4DSITNFI6NO6H}

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	2026-05-18T02:21:36.269360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6568d1d7295abcf5f07244da5479aef1df39cfd5a8dd5e18b49a7e4bf0a300fc

Aliases

arxiv: 1109.5660 · arxiv_version: 1109.5660v3 · doi: 10.48550/arxiv.1109.5660 · pith_short_12: MVUNDVZJLK6P · pith_short_16: MVUNDVZJLK6PL4DS · pith_short_8: MVUNDVZJ

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/MVUNDVZJLK6PL4DSITNFI6NO6H \
  | 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: 6568d1d7295abcf5f07244da5479aef1df39cfd5a8dd5e18b49a7e4bf0a300fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af1248d8d91e1fd909b3d8e4c33df2f4ae3f3053c00c0e8131be2b57cc5f64c2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2011-09-26T18:19:31Z",
    "title_canon_sha256": "3e93fce984c37826a7b16887e72197e8b7c237d17efa7bc5b891158270d2aae8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5660",
    "kind": "arxiv",
    "version": 3
  }
}