Pith Number

pith:X7TMDBWF

pith:2012:X7TMDBWFLF2MKOXJXNWWP5VP37

not attested not anchored not stored refs pending

Some quantitative results on Lipschitz inverse and implicit functions theorems

Phan Phien

arxiv:1204.4916 v2 · 2012-04-22 · math.NA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X7TMDBWFLF2MKOXJXNWWP5VP37}

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.

Cited by

2 papers in Pith

CBARA: Covariate-Balanced-and-Adjusted Response-Adaptive Randomization

Receipt and verification

First computed	2026-05-18T03:56:45.915869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfe6c186c55974c53ae9bb6d67f6afdff6129752c046040d3e4444620248276b

Aliases

arxiv: 1204.4916 · arxiv_version: 1204.4916v2 · doi: 10.48550/arxiv.1204.4916 · pith_short_12: X7TMDBWFLF2M · pith_short_16: X7TMDBWFLF2MKOXJ · pith_short_8: X7TMDBWF

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/X7TMDBWFLF2MKOXJXNWWP5VP37 \
  | 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: bfe6c186c55974c53ae9bb6d67f6afdff6129752c046040d3e4444620248276b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09617b745956eaf6da0789328f9433029c7aa31f415741637aea6069ce141ae7",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-04-22T17:27:46Z",
    "title_canon_sha256": "fd998ac640087821d7a637ef9f2c4aea05b5bf3d93483cbeb09d3b4240f98b86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4916",
    "kind": "arxiv",
    "version": 2
  }
}