Pith Number

pith:45YP4Z5W

pith:2007:45YP4Z5WM3M4I5GPBXFHIRHQMV

not attested not anchored not stored refs pending

A Short Proof of the VPN Tree Routing Conjecture on Ring Networks

Fabrizio Grandoni, Gianpaolo Oriolo, Martin Skutella, Volker Kaibel

arxiv:0710.3044 v2 · 2007-10-16 · math.CO · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45YP4Z5WM3M4I5GPBXFHIRHQMV}

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	2026-05-18T04:09:14.077950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e770fe67b666d9c474cf0dca7444f06558b3cf2327c04f8d4d13c9a25379ebdf

Aliases

arxiv: 0710.3044 · arxiv_version: 0710.3044v2 · doi: 10.48550/arxiv.0710.3044 · pith_short_12: 45YP4Z5WM3M4 · pith_short_16: 45YP4Z5WM3M4I5GP · pith_short_8: 45YP4Z5W

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/45YP4Z5WM3M4I5GPBXFHIRHQMV \
  | 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: e770fe67b666d9c474cf0dca7444f06558b3cf2327c04f8d4d13c9a25379ebdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76d922c68d021657b338b1bba47b41b38a4a42d6b04a74471650c2f637d37f9a",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-10-16T13:08:15Z",
    "title_canon_sha256": "6d05bf0d7cd5be2391ea2277b1a60c7710f79e133fdb6d80eb500fad42e1921d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.3044",
    "kind": "arxiv",
    "version": 2
  }
}