{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ELFPAZMIYCLFNIGMU3TR5IDZMR","short_pith_number":"pith:ELFPAZMI","canonical_record":{"source":{"id":"2410.04121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-05T11:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"6b3e1cff34199311399582892e921c955fca01bef17dc7321f43e2f506740ec4","abstract_canon_sha256":"52cd9d1ba9edcb339ddf85356d5c73eb135d214e1847e8162693e7c92c70cccd"},"schema_version":"1.0"},"canonical_sha256":"22caf06588c09656a0cca6e71ea07964721988b2981923c8a2cc5fbd03643174","source":{"kind":"arxiv","id":"2410.04121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.04121","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.04121v1","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.04121","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"ELFPAZMIYCLF","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_16","alias_value":"ELFPAZMIYCLFNIGM","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_8","alias_value":"ELFPAZMI","created_at":"2026-07-05T09:16:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ELFPAZMIYCLFNIGMU3TR5IDZMR","target":"record","payload":{"canonical_record":{"source":{"id":"2410.04121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-05T11:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"6b3e1cff34199311399582892e921c955fca01bef17dc7321f43e2f506740ec4","abstract_canon_sha256":"52cd9d1ba9edcb339ddf85356d5c73eb135d214e1847e8162693e7c92c70cccd"},"schema_version":"1.0"},"canonical_sha256":"22caf06588c09656a0cca6e71ea07964721988b2981923c8a2cc5fbd03643174","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:16:29.363366Z","signature_b64":"pVSYJor+cNtJRklv8K4YnZ4xbKW+ysHVbWjmyFmgnSYUATxIAm0yC97V+eNByRLWAPSuru2WGnBoUztSsMzIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22caf06588c09656a0cca6e71ea07964721988b2981923c8a2cc5fbd03643174","last_reissued_at":"2026-07-05T09:16:29.362893Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:16:29.362893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.04121","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":"2026-07-05T09:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IhNALBP2xet9/QOelIlQxl94p2RRwt2rd/d5/E1FwIxGf5zCznXi4SihMsWwUzio6LmZzjvPxRdWw4oUFeSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T22:29:22.063334Z"},"content_sha256":"2a0c882601d3015a8e61abc6d50088823f7b790ad9926cc376c160d24b75da9a","schema_version":"1.0","event_id":"sha256:2a0c882601d3015a8e61abc6d50088823f7b790ad9926cc376c160d24b75da9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ELFPAZMIYCLFNIGMU3TR5IDZMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volume growth functions of complete Riemannian manifolds with positive scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anushree Das, Soma Maity","submitted_at":"2024-10-05T11:05:22Z","abstract_excerpt":"Let $M$ be an open manifold of dimension at least $3$, which admits a complete metric of positive scalar curvature. For a function $v$ with bounded growth of derivative, whether $M$ admits a metric of positive scalar curvature with volume growth of the same growth type as $v$ is unknown. We answer this question positively in the case of manifolds, which are infinite connected sums of closed manifolds that admit metrics of positive scalar curvature. To define a metric of positive scalar curvature with a certain volume growth type on $M$, we use the Gromov-Lawson construction of metrics with pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04121","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/2410.04121/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":"2026-07-05T09:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZgOAgPkgJW9ffSfQlHU/2r0yn6sK9fChY9nk2n0mW+j8GLQcTIG6qG3EzgsjOQhsWLK1pFiNG7k+2sBW6YzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T22:29:22.063836Z"},"content_sha256":"8f4435ddef40a60129041931792738e3643e2acbc562ce046042a9690a6abcef","schema_version":"1.0","event_id":"sha256:8f4435ddef40a60129041931792738e3643e2acbc562ce046042a9690a6abcef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/bundle.json","state_url":"https://pith.science/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/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":"2026-08-07T22:29:22Z","links":{"resolver":"https://pith.science/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR","bundle":"https://pith.science/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/bundle.json","state":"https://pith.science/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELFPAZMIYCLFNIGMU3TR5IDZMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ELFPAZMIYCLFNIGMU3TR5IDZMR","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":"52cd9d1ba9edcb339ddf85356d5c73eb135d214e1847e8162693e7c92c70cccd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-05T11:05:22Z","title_canon_sha256":"6b3e1cff34199311399582892e921c955fca01bef17dc7321f43e2f506740ec4"},"schema_version":"1.0","source":{"id":"2410.04121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.04121","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"2410.04121v1","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.04121","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"ELFPAZMIYCLF","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_16","alias_value":"ELFPAZMIYCLFNIGM","created_at":"2026-07-05T09:16:29Z"},{"alias_kind":"pith_short_8","alias_value":"ELFPAZMI","created_at":"2026-07-05T09:16:29Z"}],"graph_snapshots":[{"event_id":"sha256:8f4435ddef40a60129041931792738e3643e2acbc562ce046042a9690a6abcef","target":"graph","created_at":"2026-07-05T09:16:29Z","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/2410.04121/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $M$ be an open manifold of dimension at least $3$, which admits a complete metric of positive scalar curvature. For a function $v$ with bounded growth of derivative, whether $M$ admits a metric of positive scalar curvature with volume growth of the same growth type as $v$ is unknown. We answer this question positively in the case of manifolds, which are infinite connected sums of closed manifolds that admit metrics of positive scalar curvature. To define a metric of positive scalar curvature with a certain volume growth type on $M$, we use the Gromov-Lawson construction of metrics with pos","authors_text":"Anushree Das, Soma Maity","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-05T11:05:22Z","title":"Volume growth functions of complete Riemannian manifolds with positive scalar curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04121","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":"sha256:2a0c882601d3015a8e61abc6d50088823f7b790ad9926cc376c160d24b75da9a","target":"record","created_at":"2026-07-05T09:16:29Z","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":"52cd9d1ba9edcb339ddf85356d5c73eb135d214e1847e8162693e7c92c70cccd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-10-05T11:05:22Z","title_canon_sha256":"6b3e1cff34199311399582892e921c955fca01bef17dc7321f43e2f506740ec4"},"schema_version":"1.0","source":{"id":"2410.04121","kind":"arxiv","version":1}},"canonical_sha256":"22caf06588c09656a0cca6e71ea07964721988b2981923c8a2cc5fbd03643174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22caf06588c09656a0cca6e71ea07964721988b2981923c8a2cc5fbd03643174","first_computed_at":"2026-07-05T09:16:29.362893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:16:29.362893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pVSYJor+cNtJRklv8K4YnZ4xbKW+ysHVbWjmyFmgnSYUATxIAm0yC97V+eNByRLWAPSuru2WGnBoUztSsMzIDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:16:29.363366Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.04121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a0c882601d3015a8e61abc6d50088823f7b790ad9926cc376c160d24b75da9a","sha256:8f4435ddef40a60129041931792738e3643e2acbc562ce046042a9690a6abcef"],"state_sha256":"5bbf86c4d1b995afa219a965a2cee028f7e60d41973558a0ea8ae78176cb74ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BSwV2sgDSlLUELbKdFjgn9bkcsh/rlh9hwHbkGzEbr3xZYsTX+MXIuMycHfLJuLOtokSTYu7GywhwChbuM+rCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T22:29:22.067618Z","bundle_sha256":"f8f99e32c12c0ffe00eb5a0b606ba4651d654c00581fbf1f4a5db0e0c82deb6b"}}