{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LYQKGHV4I6A2IA4L35HU4E4ACG","short_pith_number":"pith:LYQKGHV4","canonical_record":{"source":{"id":"2109.05027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-10T18:00:01Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d35559a6d8998d1a382e57168a3153b23f44087f444240aaddcee32ec0963775","abstract_canon_sha256":"ebbca3a58cbef907ad8d81bb9e5df0837c17f9e64f6356768e5a57dc29a82cae"},"schema_version":"1.0"},"canonical_sha256":"5e20a31ebc4781a4038bdf4f4e1380119287056a7ea7d7e0958e21002f7c0b4d","source":{"kind":"arxiv","id":"2109.05027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.05027","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"2109.05027v1","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.05027","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"LYQKGHV4I6A2","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_16","alias_value":"LYQKGHV4I6A2IA4L","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_8","alias_value":"LYQKGHV4","created_at":"2026-07-05T03:36:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LYQKGHV4I6A2IA4L35HU4E4ACG","target":"record","payload":{"canonical_record":{"source":{"id":"2109.05027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-10T18:00:01Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d35559a6d8998d1a382e57168a3153b23f44087f444240aaddcee32ec0963775","abstract_canon_sha256":"ebbca3a58cbef907ad8d81bb9e5df0837c17f9e64f6356768e5a57dc29a82cae"},"schema_version":"1.0"},"canonical_sha256":"5e20a31ebc4781a4038bdf4f4e1380119287056a7ea7d7e0958e21002f7c0b4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:14.544192Z","signature_b64":"q10VvAFJBpgMKGFAZYV5T4uzAiyKNHx+q6cipEQiywbixIEPPEsn2/Slssw/mW3HQQfat6C5+/n79cP6LujkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e20a31ebc4781a4038bdf4f4e1380119287056a7ea7d7e0958e21002f7c0b4d","last_reissued_at":"2026-07-05T03:36:14.543728Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:14.543728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.05027","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZrruF9ZEEbqh0muAs1Kl2EjRyOpTILqINHPlG938W5GboQknttIlJwHLbXH/KQm8QkhxEg9ulNd3UytabBHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:52:39.896759Z"},"content_sha256":"2dd4fd91d9326a73c11f3537335cc59e6d004fe205427fcb9e4003a9f3bb94b0","schema_version":"1.0","event_id":"sha256:2dd4fd91d9326a73c11f3537335cc59e6d004fe205427fcb9e4003a9f3bb94b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LYQKGHV4I6A2IA4L35HU4E4ACG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Alexandre M. Pombo, Carlos A. R. Herdeiro, Eugen Radu, Jo\\~ao M. S. Oliveira","submitted_at":"2021-09-10T18:00:01Z","abstract_excerpt":"Virial (aka scaling) identities are integral identities that are useful for a variety of purposes in non-linear field theories, including establishing no-go theorems for solitonic and black hole solutions, as well as for checking the accuracy of numerical solutions. In this paper, we provide a pedagogical rationale for the derivation of such integral identities, starting from the standard variational treatment of particle mechanics. In the framework of one-dimensional (1D) effective actions, the treatment presented here yields a set of useful formulas for computing virial identities in any fie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.05027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.05027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wr6IVwtp1XdAs5cYCAxOZDoKsdTecLJRx3F2W6W3Jw+qpGSY61GW4gtiNWcC8zfvUmwksJVLUzV38QtpAd7JCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:52:39.897366Z"},"content_sha256":"2bba1ff3f35551a0dfde47b07542872088bd073ed01f0240d04ea7119c245768","schema_version":"1.0","event_id":"sha256:2bba1ff3f35551a0dfde47b07542872088bd073ed01f0240d04ea7119c245768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/bundle.json","state_url":"https://pith.science/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-08T07:52:39Z","links":{"resolver":"https://pith.science/pith/LYQKGHV4I6A2IA4L35HU4E4ACG","bundle":"https://pith.science/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/bundle.json","state":"https://pith.science/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYQKGHV4I6A2IA4L35HU4E4ACG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LYQKGHV4I6A2IA4L35HU4E4ACG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ebbca3a58cbef907ad8d81bb9e5df0837c17f9e64f6356768e5a57dc29a82cae","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-10T18:00:01Z","title_canon_sha256":"d35559a6d8998d1a382e57168a3153b23f44087f444240aaddcee32ec0963775"},"schema_version":"1.0","source":{"id":"2109.05027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.05027","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"2109.05027v1","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.05027","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"LYQKGHV4I6A2","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_16","alias_value":"LYQKGHV4I6A2IA4L","created_at":"2026-07-05T03:36:14Z"},{"alias_kind":"pith_short_8","alias_value":"LYQKGHV4","created_at":"2026-07-05T03:36:14Z"}],"graph_snapshots":[{"event_id":"sha256:2bba1ff3f35551a0dfde47b07542872088bd073ed01f0240d04ea7119c245768","target":"graph","created_at":"2026-07-05T03:36:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.05027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Virial (aka scaling) identities are integral identities that are useful for a variety of purposes in non-linear field theories, including establishing no-go theorems for solitonic and black hole solutions, as well as for checking the accuracy of numerical solutions. In this paper, we provide a pedagogical rationale for the derivation of such integral identities, starting from the standard variational treatment of particle mechanics. In the framework of one-dimensional (1D) effective actions, the treatment presented here yields a set of useful formulas for computing virial identities in any fie","authors_text":"Alexandre M. Pombo, Carlos A. R. Herdeiro, Eugen Radu, Jo\\~ao M. S. Oliveira","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-10T18:00:01Z","title":"Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.05027","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2dd4fd91d9326a73c11f3537335cc59e6d004fe205427fcb9e4003a9f3bb94b0","target":"record","created_at":"2026-07-05T03:36:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ebbca3a58cbef907ad8d81bb9e5df0837c17f9e64f6356768e5a57dc29a82cae","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-10T18:00:01Z","title_canon_sha256":"d35559a6d8998d1a382e57168a3153b23f44087f444240aaddcee32ec0963775"},"schema_version":"1.0","source":{"id":"2109.05027","kind":"arxiv","version":1}},"canonical_sha256":"5e20a31ebc4781a4038bdf4f4e1380119287056a7ea7d7e0958e21002f7c0b4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e20a31ebc4781a4038bdf4f4e1380119287056a7ea7d7e0958e21002f7c0b4d","first_computed_at":"2026-07-05T03:36:14.543728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:36:14.543728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q10VvAFJBpgMKGFAZYV5T4uzAiyKNHx+q6cipEQiywbixIEPPEsn2/Slssw/mW3HQQfat6C5+/n79cP6LujkBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:36:14.544192Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.05027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd4fd91d9326a73c11f3537335cc59e6d004fe205427fcb9e4003a9f3bb94b0","sha256:2bba1ff3f35551a0dfde47b07542872088bd073ed01f0240d04ea7119c245768"],"state_sha256":"55b527f1a9630bc4d6442aa435c5f6a6cdf0ac17259e33ef78883d9d2c9d44e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbuGyNB/8y5A1P4cG1vQFZbnxH6dx5b578Vm/P+RaRvD6j0nvfZ1rrtnUZFOgTib+E7KM8e4E4prsL0VfycLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T07:52:39.901301Z","bundle_sha256":"307d3a34e1f317373270330acde2babf10db5d466feb8435d7deb9dd0697e474"}}