Pith Number

pith:MM3G5RPV

pith:2006:MM3G5RPVWLPJEJVBVWHIQZ5V4R

not attested not anchored not stored refs pending

Transition from a network of thin fibers to the quantum graph: an explicitly solvable model

B. Vainberg, S. Molchanov

arxiv:math-ph/0605037 v1 · 2006-05-11 · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MM3G5RPVWLPJEJVBVWHIQZ5V4R}

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	2026-05-18T01:17:53.740713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63366ec5f5b2de9226a1ad8e8867b5e4475ad89028b10a8ac28e5973231521af

Aliases

arxiv: math-ph/0605037 · arxiv_version: math-ph/0605037v1 · doi: 10.48550/arxiv.math-ph/0605037 · pith_short_12: MM3G5RPVWLPJ · pith_short_16: MM3G5RPVWLPJEJVB · pith_short_8: MM3G5RPV

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/MM3G5RPVWLPJEJVBVWHIQZ5V4R \
  | 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: 63366ec5f5b2de9226a1ad8e8867b5e4475ad89028b10a8ac28e5973231521af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eba7015fe3f0b24aad9d6ba79db1b46ac60045290f444e777b7e98cde4a3b8d7",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-05-11T02:09:53Z",
    "title_canon_sha256": "621beea7fbf3e83ee714f1d14dec5cc40654a3a4fa8eb7a846bb2598e3bae9a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0605037",
    "kind": "arxiv",
    "version": 1
  }
}