Pith Number

pith:YVNUYMJW

pith:2009:YVNUYMJWMNMP66CK5XHDP463UI

not attested not anchored not stored refs pending

Monotonic functions in Bianchi models: Why they exist and how to find them

Claes Uggla, J. Mark Heinzle

arxiv:0907.0653 v2 · 2009-07-03 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YVNUYMJWMNMP66CK5XHDP463UI}

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	2026-05-18T02:13:05.443557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c55b4c31366358ff784aedce37f3dba22a9a6c81c2c361ab7065253440842a63

Aliases

arxiv: 0907.0653 · arxiv_version: 0907.0653v2 · doi: 10.48550/arxiv.0907.0653 · pith_short_12: YVNUYMJWMNMP · pith_short_16: YVNUYMJWMNMP66CK · pith_short_8: YVNUYMJW

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/YVNUYMJWMNMP66CK5XHDP463UI \
  | 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: c55b4c31366358ff784aedce37f3dba22a9a6c81c2c361ab7065253440842a63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64f9ed0ad1566106a5739ee473249135aac049c25eaf9f205eb83bda50ce83ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2009-07-03T15:39:25Z",
    "title_canon_sha256": "2075a8bc1ec557f7114c57806b11ef6d08a14055adb4161ed135347cdbc8b1bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0653",
    "kind": "arxiv",
    "version": 2
  }
}