# Priority-search documentation (ancillary file)

Companion to "Memory back-reaction in black-hole scattering at fifth
post-Minkowskian order" (M. D. Schwartz, 2026). This file documents the
literature searches behind two statements of the paper:

1. **The bound-kinematics statement** (Sec. 6): to our knowledge the full
   Frobenius bases of the Apery K3' and 4F3 geometries had not been
   evaluated at bound kinematics before. Backed by the search of Part A
   below (run 2026-07-15), which covers the wider K3/Calabi-Yau sector and
   therefore this narrower statement.
2. **The statement on the dissipative 5PM-2SF sector** (Sec. 1): the
   conservative 5PM-2SF papers name radiation reaction, radiated energy and
   recoil at this order as the next step, and to our knowledge no results
   for them have appeared. Backed by the arXiv and conference searches of
   Part B (2026-07-14, 2026-07-16, 2026-07-17).

Every query below is verbatim and can be rerun; every result is dated.
Searches were run against the public arXiv API
(https://export.arxiv.org/api/query), the INSPIRE-HEP API, indico.global,
and general web search, as indicated per item.

---

## Part A: Search for prior bound-kinematics continuations (run 2026-07-15)

Question searched: does any paper analytically continue the K3/Calabi-Yau
period sector of post-Minkowskian integrals to bound kinematics
(gamma < 1, unit-circle x)? Result: **no such paper found** (as of
2026-07-15). Three independent evidence lines.

### A.1 Citation search (INSPIRE)

- All **115** INSPIRE-listed citers of arXiv:2411.11846 (recid 2849596)
  scanned by title; all **55** citers of arXiv:2401.07899 (recid 2747205)
  scanned by title.
- Fulltext-filtered citer subsets checked paper-by-paper:
  `refersto ... and ft "boundary-to-bound"` -> 17 hits;
  `ft "bound orbit"` -> 19 hits; `ft "periastron"` -> 10 hits.
  Hits included 2503.23317, 2606.24432, 2506.20665, 2602.10089,
  2604.25916, 2604.09545, 2603.05237, 2512.02274. None performs the
  continuation.

### A.2 Zero-result cross-searches

arXiv API (verbatim, both returned **0** results):

    abs:"Calabi-Yau" AND abs:"bound orbits"
    abs:"K3" AND abs:"bound orbits"

INSPIRE fulltext (verbatim, **0** records all-INSPIRE):

    ft "bound kinematics" and ft "Calabi-Yau"

INSPIRE fulltext, related nonzero control:
`ft "Calabi-Yau" and ft "boundary-to-bound"` -> 17 all-INSPIRE, each
checked, none relevant to the target combination.

### A.3 Web searches (verbatim, all NULL for the target combination)

1. `"boundary to bound" Calabi-Yau`: pure-math CY-with-boundary hits only.
2. `"boundary-to-bound" "Calabi-Yau" post-Minkowskian`: surfaces
   2312.11371 / 2411.11846 / 2503.20655, no B2B connection.
3. `K3 periods bound orbits post-Minkowskian gravity`: 2601.16256
   (scattering), 2402.00124 (no CY).
4. `analytic continuation radiated energy 5PM bound orbits`: 2402.00124,
   2404.03607.
5. `Calabi-Yau periods elliptic orbits gravitational waves`: press
   coverage only.
6. `"unit circle" analytic continuation post-Minkowskian gamma bound orbit`
  : generic B2B hits.
7. `Apery K3 gravity bound orbit`: disconnected math/astro.
8. `Dlapa Kalin Liu Porto local-in-time fourth post-Minkowskian bound
   orbits tail analytic continuation`: the adjacent DKLP line confirmed
   (2112.11296, 2403.04853, 2506.20665, 2604.25916); local part only.
9. `periastron advance Calabi-Yau post-Minkowskian`: the two literatures
   appear only separately.
10. `eccentric binaries 5PM radiated energy Calabi-Yau bound`: only
    2411.11846's outlook sentence.
11. `Weinzierl OR Pögel OR Frellesvig OR Nega Calabi-Yau periods "bound"
    kinematics analytic continuation 2025`: all 2025-26 output of that
    cluster is scattering-side/QFT kinematics.
12. `"Calabi-Yau" "bound orbits" gravitational two-body continuation`: null.
13. `"unit circle" K3 period "analytic continuation" Feynman integral gamma
    "bound"`: surfaces Bogner-Schweitzer-Weinzierl 1705.08952/1807.02542
    (method neighbor: elliptic Feynman integrals on |q| <= 1, never applied
    to PM gamma < 1).

### A.4 The sources themselves declare it open

- arXiv:2411.11846, abstract (local TeX, line 292), future tense, no
  citation: the transition to the bound-state problem "will need to be
  performed."
- arXiv:2601.16256 and arXiv:2505.10274 do not discuss bound continuation.
- arXiv:2401.07899's only continuations stay on the scattering branch
  (past x = 1 to the inverse branch, and to the second MUM point): never
  onto |x| = 1.

### A.5 Nearest neighbors individually cleared

2603.05237 (bound WQFT matrix elements, 3PL polylog), 2503.23317
(probe-limit Schwarzschild, different function space), 2606.11423,
2604.25916, 2506.20665, 2512.16098, 2602.10089 (resummation, defers to an
unbound-to-bound mapping that does not exist at this order), 2603.15383
(conservative-sector cancellation), 2112.11296 (conservative B2B carries
complete elliptic integrals K, E: conservative sector), 2402.00124
(tree-level waveform + 3PM fluxes in rapidity; "nontrivial at 4PM and
beyond due to nonlocal-in-time contributions from the tail effect").

Verification depth per paper: abstracts fetched for 18 papers, e-print TeX
downloaded and quoted verbatim for 5, local TeX source quoted for 4.

---

## Part B: Searches for dissipative 5PM-2SF results

Queries run against arXiv categories gr-qc + hep-th, sortBy=submittedDate
descending. Each search looked for (i) dissipative or radiative 5PM-2SF
master integrals or observables; (ii) public 2SF coefficient tables.

### B.1 Search 1: 2026-07-14

Web searches (verbatim):

1. `dissipative "5PM" "2SF" radiated energy recoil black hole scattering
   2026`: no dissipative 2SF paper; newest 2SF item remains 2601.16256
   (conservative); 2507.03442 is 1SF-exact GSF, not 2SF.
2. `arXiv July 2026 fifth post-Minkowskian second self-force radiative
   impulse worldline`: same negative; surfaced the PRL page
   (journals.aps.org, DOI 10.1103/zjcp-ssrw) confirming 2512.23654
   published 2026-07-06, potential-only.

As of 2026-07-14: no dissipative 5PM-2SF publication; the Amplitudes 2026
contribution list (QMUL, June 29 - July 3) announces no dissipative-2SF or
6PM result.

### B.2 Search 2: executed 2026-07-15, 20:09-20:12 UTC

arXiv API queries, verbatim `search_query` strings as issued (date-read
stamps as recorded):

| # | date-read (UTC) | search_query (verbatim) | totalResults |
|---|---|---|---|
| q1 | 2026-07-15T20:09:34Z | `(cat:gr-qc OR cat:hep-th) AND all:"fifth post-Minkowskian" AND (all:dissipative OR all:radiative OR all:"radiation reaction" OR all:"radiated energy" OR all:recoil)` | 4 |
| q2 | 2026-07-15T20:09:38Z | `(cat:gr-qc OR cat:hep-th) AND all:"5PM" AND all:"2SF"` | 5 |
| q3 | 2026-07-15T20:09:41Z | `(cat:gr-qc OR cat:hep-th) AND all:"second self-force" AND all:scattering` | 3 |
| q4 | 2026-07-15T20:09:45Z | `abs:"O(G^5)" AND (abs:radiative OR abs:dissipative)` | 1 |
| q5 | 2026-07-15T20:09:49Z | `(cat:gr-qc OR cat:hep-th) AND (au:Driesse OR au:Jakobsen OR au:Mogull OR au:Nega OR au:Plefka OR au:Sauer OR au:Usovitsch OR au:Klemm)` | 357 (top 40 pulled) |
| q6 | 2026-07-15T20:09:53Z | `(cat:gr-qc OR cat:hep-th) AND (au:Bern OR au:Ruf OR au:Jackman OR au:Mansfield OR au:Dlapa OR au:Kaelin OR au:Kalin OR au:Porto)` | 331 (top 40) |
| q7 | 2026-07-15T20:09:56Z | `(cat:gr-qc OR cat:hep-th) AND (au:Frellesvig OR au:Morales OR au:Wilhelm OR au:Poegel OR au:Pogel OR au:Weinzierl)` | 461 (top 40) |
| q8 | 2026-07-15T20:10:01Z | `(cat:gr-qc OR cat:hep-th) AND submittedDate:[202607131800 TO 202607162359]` | 55 |

q8 is a full window listing (every gr-qc/hep-th submission in the window,
no topic filter), searched for 24 author surnames and 19 subject keywords
and read title by title (55/55). The window starts at 2026-07-13 18:00 UTC
to overlap search 1.

In-window items examined (each classified against its actual abstract):

1. **arXiv:2601.16256 v4** (replaced 2026-07-13 19:47:59 UTC): comment
   "version to be published in PRL"; abstract unchanged in scope
   (conservative only). The Zenodo ancillary record (18340334) has latest
   version 19680912 v2, published 2026-04-21, conservative only; the
   changelog is a Mathematica loader bugfix. Not a dissipative result
   (replacement of the known conservative paper on acceptance in PRL).
2. **arXiv:2607.12033** (Guan, Mistlberger, Ruf): 3-loop QCD Higgs+3
   partons. Matches the author query (Ruf) but is not post-Minkowskian;
   the "Bern" match is a substring of *Bern*hard Mistlberger, and Zvi Bern
   is not an author. Not relevant.
3. **arXiv:2607.12973** (Damgaard, Kim, Lee): "Recursion Relations for
   Classical Gravity", demonstrated to 3PM including radiation
   back-reaction. Not 5PM-2SF. Not relevant.
4. Remaining 52 window entries: no post-Minkowskian scattering content.

Conferences:

- **Amplitudes 2026** (QMUL, 2026-06-29 to 07-03; indico.global event
  16407; contribution list read 2026-07-15T20:11:27Z; 40 contributions;
  slides read):
  - Jakobsen, "Advances in High-Precision Gravitational Scattering from
    Worldline QFT": presents the CONSERVATIVE 2SF angle (2601.16256);
    outlook slide (37/38): "Dissipative effects at 5PM-2SF: Building on
    [GUJ, K. Stoldt: 2605.12214]": declared in progress, NOT results.
  - Bern, "Progress at the 5th post-Minkowskian Order in Gravitational-Wave
    Physics": staging slide 20: "5. 2SF dissipative effects. To be done"
    (names both his group and the Berlin group); summary slide 34: "5PM
    radiative, dissipative contributions under study." Declared in
    progress, NOT results.
  - No other contribution matched the 5PM, dissipative or author searches.
- **QCD Meets Gravity 2026** (DESY indico event 54372, read
  2026-07-15T20:12:24Z): December 2026 event, 0 contributions posted yet.

Result: no dissipative 5PM-2SF result found. The search ran before the
2026-07-16 00:00 UTC arXiv announcement; the window of search 3 starts at
2026-07-15 18:00 UTC to cover the gap.

### B.3 Search 3: 2026-07-17 (window from 2026-07-15T18:00Z)

q1-class query: 7 entries, newest 2603.11774 (2026-03-12, pre-window);
q2-class query: 20 entries, newest 2605.12214v2 (2026-05-12, pre-window).
In-window NEW = 0, REVISIONS = 0. 2601.16256 remains at v4, title/scope
unchanged (conservative only). Result: none found.

### B.4 Query set for later reruns

arXiv API (https://export.arxiv.org), categories gr-qc + hep-th:

    ("fifth post-Minkowskian" OR 5PM) AND (dissipative OR radiative OR
    "radiation-reacted" OR recoil OR "radiated energy")

plus the author cluster

    (Driesse, Jakobsen, Mogull, Plefka, Sauer, Usovitsch) AND
    (post-Minkowskian OR 5PM)

with both NEW postings and REVISIONS checked against the window.

---

## Part C: Records

The raw responses (Atom XML per query, the 55-entry window listing, the
conference contribution lists and slide text) were saved on the dates
given and are kept by the author.

Prepared 2026-07-17. The
searches above can be rerun by any reader from the verbatim strings; the
saved responses record what was visible on each date.