Pith Number

pith:I2PBSMLN

pith:2025:I2PBSMLN7YU33M2DST74RGJ6XP

not attested not anchored not stored refs pending

Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies

Benjamin Lyons, Connor Lane, William R. Green

arxiv:2506.08831 v1 · 2025-06-10 · math.AP · math-ph · 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{I2PBSMLN7YU33M2DST74RGJ6XP}

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	2026-07-05T11:19:13.903141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

469e19316dfe29bdb34394ffc8993ebbd9446a93bf1c3d6198dc44ac4def9c9f

Aliases

arxiv: 2506.08831 · arxiv_version: 2506.08831v1 · doi: 10.48550/arxiv.2506.08831 · pith_short_12: I2PBSMLN7YU3 · pith_short_16: I2PBSMLN7YU33M2D · pith_short_8: I2PBSMLN

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/I2PBSMLN7YU33M2DST74RGJ6XP \
  | 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: 469e19316dfe29bdb34394ffc8993ebbd9446a93bf1c3d6198dc44ac4def9c9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea12b9acaf82f94a15649721cb06bd28e6ca9517aa65bb358e5d204d7dec8b28",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-10T14:19:47Z",
    "title_canon_sha256": "5d7e0615feb5dbc1c3b3c9c888176329785a2359fd8ad3d16357763535c61018"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08831",
    "kind": "arxiv",
    "version": 1
  }
}