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Paper Citation Record · LEDGER

Metric functionals and weak convergence

As of 7 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2506.04154.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.04154 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:05:55.700678Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

  • verified exact1
  • verified fuzzy22
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e68e8666-ec89-4385-9126-128eb52d6c24 · outbound

This paper cites Deep limits and a cut-off phenomenon for neural networks.

Metric functionals and weak convergence Deep limits and a cut-off phenomenon for neural networks

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:06:00.463777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 986c4a85-3488-4bb0-9c33-cfa73c27ba4b · outbound

This paper cites Old and new challenges in Hadamard spaces.

Metric functionals and weak convergence Old and new challenges in Hadamard spaces

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:06:00.271061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation b9b7482f-fde8-4069-b27f-61cbc90de335 · outbound

This paper cites Introduction to Banach spaces and their geometry , volume 68 of North-Holland Math.

Metric functionals and weak convergence Introduction to Banach spaces and their geometry , volume 68 of North-Holland Math

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:06:00.103720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 38cb8376-7163-49ed-9f60-1c74277ba8b8 · outbound

This paper cites Horofunctions and metric compactification of noncompact Hermitian symmetric spaces.

Metric functionals and weak convergence Horofunctions and metric compactification of noncompact Hermitian symmetric spaces

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:59.958236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:53.805970Z digest=sha256:0dbe60b652f69e2e1d0582cfb7e53d47087c8a0a86e9d6f19925926687e106a9

Observation 547c6f9c-51ab-47e9-af83-ed51d9f67e56 · outbound

This paper cites Isabel Garrido, Jesus A Jaramillo, and Sebastian Tapia-Garc \'i a.

Metric functionals and weak convergence Isabel Garrido, Jesus A Jaramillo, and Sebastian Tapia-Garc \'i a

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:59.780533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:53.878993Z digest=sha256:72b8e532e2f0ad79970e02e3a9c7275eb83160925f09156d82b2b635bb25f2b8

Observation dd041711-f096-4743-99ef-09f67086e962 · outbound

This paper cites Convex geodesic bicombings and hyperbolicity.

Metric functionals and weak convergence Convex geodesic bicombings and hyperbolicity

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:59.536594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:53.951181Z digest=sha256:2c791098e12f2ad0c9e75926ce548dcf28da849af4379246877633bec7c90b52

Observation 6cf585cc-485f-456f-be0e-008001cda0c9 · outbound

This paper cites CAT \((k)\) -spaces, weak convergence and fixed points.

Metric functionals and weak convergence CAT \((k)\) -spaces, weak convergence and fixed points

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:59.290875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.060826Z digest=sha256:2f508fc38923f5c1014f6dd5c108e1df8639c9f3723fd688108a9ea581891814

Observation f2672d34-982c-4e0d-8670-6c19acc51c90 · outbound

This paper cites Subadditive and multiplicative ergodic theorems.

Metric functionals and weak convergence Subadditive and multiplicative ergodic theorems

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:59.110194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.206573Z digest=sha256:7bca32dc68ecbd335c20b8b76d41ef0a118bebdcbfd378752c54b1a6075313a5

Observation 3719d549-d879-4d79-b887-16527624f3e5 · outbound

This paper cites Guti \'e rrez and Anders Karlsson.

Metric functionals and weak convergence Guti \'e rrez and Anders Karlsson

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:58.945781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.315880Z digest=sha256:688210fa61398d13ca0b4092932d35b6c640a32ce92814927149fcf0cdf1d94e

Observation db2c2ab4-e5a2-4669-b090-defeb6429d29 · outbound

This paper cites Subinvariant metric functionals for nonexpansive mappings.

Metric functionals and weak convergence Subinvariant metric functionals for nonexpansive mappings

Reference 10

Resolution
metadata mismatch
local_arxiv, observed 2026-08-07T11:05:56.168262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.425673Z digest=sha256:e49d931c906f9ecb1b4b3982f428b855b549e2409d42aa2ab47fa7be10ed79f4

Observation 2ae24faa-6e01-450a-bf4e-6819eb12b423 · outbound

This paper cites Guti \'e rrez.

Metric functionals and weak convergence Guti \'e rrez

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:58.769848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.498124Z digest=sha256:672460ea8295b1106bd970cd974bf492562ca70408afb8dd113ea75e52673e5d

Observation be3114f1-f3ee-4c23-8784-8aa38a54e097 · outbound

This paper cites Guti \'e rrez.

Metric functionals and weak convergence Guti \'e rrez

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:58.596369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.570728Z digest=sha256:ef379f59e6b018e94951a364f4e80362eed058fbb179d78a85fe39038759d689

Observation a2ffab4a-3fd5-433e-94ba-0d7248351d54 · outbound

This paper cites A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces.

Metric functionals and weak convergence A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:58.400504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.716916Z digest=sha256:bcc7633b56cf0022c3dcb52cf2c81f4e22e5947d8f450ab6ff41a03babf92f66

Observation f15df122-649f-433f-a3f5-5b6714029420 · outbound

This paper cites Hahn- Banach for metric functionals and horofunctions.

Metric functionals and weak convergence Hahn- Banach for metric functionals and horofunctions

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:58.212092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.789579Z digest=sha256:953c2ab540eff488debb7742a22aa4c35e76dbc9046ce199fb5efccc4eecbdcf

Observation 23706e1e-55da-4dd2-b6e1-01546c8746c9 · outbound

This paper cites Elements of a metric spectral theory.

Metric functionals and weak convergence Elements of a metric spectral theory

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:57.978372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.862032Z digest=sha256:0ddbdf6fb04fc1a91b6ed1ab54a01325f8a6f3dcf3c97cf00d3ebcaea1702fc3

Observation c7173b43-6558-45f2-b53f-d3322a975507 · outbound

This paper cites A metric fixed point theorem and some of its applications.

Metric functionals and weak convergence A metric fixed point theorem and some of its applications

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:57.789172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:54.935036Z digest=sha256:e7f64a5fc9f171efa22dba8ff78866def260b71b166754db0cc4f74ced72b37c

Observation e132db21-3ffe-4c1d-a3bf-95b0f3c08288 · outbound

This paper cites an unresolved cited work.

Metric functionals and weak convergence Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:05:57.579480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.008186Z digest=sha256:07507dfb1abed466ec40fabfd150f3e9b52fc8c869a25bd92e9360045be42db3

Observation bf323a04-66c7-43da-9ea5-1393636e52b0 · outbound

This paper cites Remarks on some fixed point theorems.

Metric functionals and weak convergence Remarks on some fixed point theorems

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:57.404181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.044184Z digest=sha256:31ea7497e3ad9cfb89d4ad1c0306326e2ee5457f0d9b82bd48aa419fcea8f7b3

Observation ca3c3228-fec4-4303-9f4d-2d3e4d2a4d90 · outbound

This paper cites Nonexpansive maps with surjective displacement.

Metric functionals and weak convergence Nonexpansive maps with surjective displacement

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:57.221005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.116776Z digest=sha256:8c55e7891e166a66de15f5ab9ab451b52978779cc3e446384574fca1fa2e7637

Observation 15a4961f-c083-4543-b269-045d9888b5dc · outbound

This paper cites Detecting fixed points of nonexpansive maps by illuminating the unit ball.

Metric functionals and weak convergence Detecting fixed points of nonexpansive maps by illuminating the unit ball

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:57.036831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.189703Z digest=sha256:d7f43acf26e47169d6f7ad4458efd9d43f09d16b0bac795f097f31f955551c7a

Observation 7a006b09-5915-4ae6-9652-19f42a776d72 · outbound

This paper cites Weak topology on CAT (0) spaces.

Metric functionals and weak convergence Weak topology on CAT (0) spaces

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:56.853017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.297551Z digest=sha256:54159ba90ee02e0f2e31bcd452f8faf8c6861b704de2a220af705999af7d6bf5

Observation cfb8c0da-7c2b-497b-932c-f719d48e3791 · outbound

This paper cites Lipschitz- Free Spaces : A Topometric Approach and Group Actions.

Metric functionals and weak convergence Lipschitz- Free Spaces : A Topometric Approach and Group Actions

Reference 22

Resolution
verified exact
raw_fallback, observed 2026-08-07T11:05:55.993657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.370669Z digest=sha256:32cdc67b399d0328ed067eea331d2cad49c039989c40bab97b84d31a5d6af014

Observation 90f03361-c961-4fc3-b774-257ec3de7ef7 · outbound

This paper cites Weak convergence of bounded sequences.

Metric functionals and weak convergence Weak convergence of bounded sequences

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:56.710474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.482023Z digest=sha256:bac411f872eaa98aacca3a93600b961e63fdc7892a471e986921a8e719e365e1

Observation f608bf9a-893b-48d1-8cee-5abc8f609e63 · outbound

This paper cites A convexity in metric space and nonexpansive mappings.

Metric functionals and weak convergence A convexity in metric space and nonexpansive mappings

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:56.532116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.591959Z digest=sha256:00a293972bba5503f228ad92373bbfa60079b3f0607e8ea13b57434794da25fa

Observation b67c240b-773a-4ba4-b1ef-834a8fa920ad · outbound

This paper cites Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces.

Metric functionals and weak convergence Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:05:56.353267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T11:05:55.700678Z digest=sha256:a9f0ef01bc79845fbe791e407e92da805e40bc34b7e58afae2ac0205534b6b75

Pith citing papers

No inbound Pith citation observations are available.