Pith Number

pith:MPCVI6VJ

pith:2015:MPCVI6VJWG5W7L5F3GVHXSVMN7

not attested not anchored not stored refs pending

Path lifting properties and embedding between RAAGs

Eon-Kyung Lee, Sang-Jin Lee

arxiv:1507.06859 v2 · 2015-07-24 · 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{MPCVI6VJWG5W7L5F3GVHXSVMN7}

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	2026-05-18T01:24:32.867004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63c5547aa9b1bb6fafa5d9aa7bcaac6fdfb8dbc74f52f6ee1a457614f3a3a86b

Aliases

arxiv: 1507.06859 · arxiv_version: 1507.06859v2 · doi: 10.48550/arxiv.1507.06859 · pith_short_12: MPCVI6VJWG5W · pith_short_16: MPCVI6VJWG5W7L5F · pith_short_8: MPCVI6VJ

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/MPCVI6VJWG5W7L5F3GVHXSVMN7 \
  | 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: 63c5547aa9b1bb6fafa5d9aa7bcaac6fdfb8dbc74f52f6ee1a457614f3a3a86b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df044dcdd93ad348f9c00c9cba20224f4f5a581e78d4a2475cc4794ed8642e1b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-07-24T14:32:02Z",
    "title_canon_sha256": "ee4ee6d222f22fc446d1f9494ce67dfab31a5f19fff20013ad677b9e65fc2a84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06859",
    "kind": "arxiv",
    "version": 2
  }
}