Pith Number

pith:WWVBBGQD

pith:2021:WWVBBGQDHNDWW4DM7CRVCRZKTF

not attested not anchored not stored refs pending

Approximate controllability of fractional order non-instantaneous impulsive functional evolution equations with state-dependent delay in Banach spaces

J. Dabas, M. T. Mohan, S. Arora

arxiv:2106.02939 v1 · 2021-06-05 · 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{WWVBBGQDHNDWW4DM7CRVCRZKTF}

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	2026-07-05T02:46:32.025013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5aa109a033b476b706cf8a351472a996e2322e5e687a1a184a7e4ab9f397cb0

Aliases

arxiv: 2106.02939 · arxiv_version: 2106.02939v1 · doi: 10.48550/arxiv.2106.02939 · pith_short_12: WWVBBGQDHNDW · pith_short_16: WWVBBGQDHNDWW4DM · pith_short_8: WWVBBGQD

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/WWVBBGQDHNDWW4DM7CRVCRZKTF \
  | 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: b5aa109a033b476b706cf8a351472a996e2322e5e687a1a184a7e4ab9f397cb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d857f07278dd8ab4471f166fb4ab3bb033b9dfbad30c400e8d903d2af2f65d9b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-06-05T17:48:05Z",
    "title_canon_sha256": "51556f49e71dc628532dcfdb84bf40789deee6eff6bbbead2ca9e90dbb8b7d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.02939",
    "kind": "arxiv",
    "version": 1
  }
}