{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J4B37JBNKMD22EB3KNFEQ2YY2F","short_pith_number":"pith:J4B37JBN","canonical_record":{"source":{"id":"1405.0827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-05T08:54:22Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"f255122dc06deaa1f18a4a1ac4aa490bcf7d56a65f9ce9068f38d8f26b242b58","abstract_canon_sha256":"adaf4f53248311691c8f894e815090e9273b8c8a2fdce5db4d38822e6cc5febf"},"schema_version":"1.0"},"canonical_sha256":"4f03bfa42d5307ad103b534a486b18d16eb9faa2758ae44f29309eb0e2d7ab40","source":{"kind":"arxiv","id":"1405.0827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0827","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0827v1","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0827","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"J4B37JBNKMD2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J4B37JBNKMD22EB3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J4B37JBN","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J4B37JBNKMD22EB3KNFEQ2YY2F","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-05T08:54:22Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"f255122dc06deaa1f18a4a1ac4aa490bcf7d56a65f9ce9068f38d8f26b242b58","abstract_canon_sha256":"adaf4f53248311691c8f894e815090e9273b8c8a2fdce5db4d38822e6cc5febf"},"schema_version":"1.0"},"canonical_sha256":"4f03bfa42d5307ad103b534a486b18d16eb9faa2758ae44f29309eb0e2d7ab40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:40.584207Z","signature_b64":"4TsUd19yfUk48l2f40AUspUeAxcbRfrNQcyxZHRrepx6NKlwWaYsZvCowW7VkdF0SXPzqe4iR2ejfxAnwJseCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f03bfa42d5307ad103b534a486b18d16eb9faa2758ae44f29309eb0e2d7ab40","last_reissued_at":"2026-05-18T02:52:40.583794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:40.583794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0827","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":"2026-05-18T02:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPx71IanVVHSwWGCv0e22eJdBCObwOBhZrzmFXzTUA0xu4YS/fSGkRYmg+DzrFB/N8UOXbjtFhkluxgEA/YHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:04:39.614492Z"},"content_sha256":"3d1dcc5fe05b81cc90da0f00a95d3b1c0fb04ad08edf078cb6e19b94f7bc7537","schema_version":"1.0","event_id":"sha256:3d1dcc5fe05b81cc90da0f00a95d3b1c0fb04ad08edf078cb6e19b94f7bc7537"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J4B37JBNKMD22EB3KNFEQ2YY2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Mauro Carfora","submitted_at":"2014-05-05T08:54:22Z","abstract_excerpt":"Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by N. Gigli and C. Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between non-linear sigma m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0827","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":""},"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":"2026-05-18T02:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Olrj30xnioFQaK4OxW3ixCK4Mc9daAGcKvCtywyRgNiFc+aIN9ACDoobPd4Vrb/aSnjO64s+ZYxBbBG8/0DDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:04:39.615227Z"},"content_sha256":"2af2f9ff58207c6de6b23d20eb38f61e23ca977836dac6d7a8e369f1dbc4f02a","schema_version":"1.0","event_id":"sha256:2af2f9ff58207c6de6b23d20eb38f61e23ca977836dac6d7a8e369f1dbc4f02a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/bundle.json","state_url":"https://pith.science/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/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":"2026-06-09T02:04:39Z","links":{"resolver":"https://pith.science/pith/J4B37JBNKMD22EB3KNFEQ2YY2F","bundle":"https://pith.science/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/bundle.json","state":"https://pith.science/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4B37JBNKMD22EB3KNFEQ2YY2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J4B37JBNKMD22EB3KNFEQ2YY2F","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":"adaf4f53248311691c8f894e815090e9273b8c8a2fdce5db4d38822e6cc5febf","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-05T08:54:22Z","title_canon_sha256":"f255122dc06deaa1f18a4a1ac4aa490bcf7d56a65f9ce9068f38d8f26b242b58"},"schema_version":"1.0","source":{"id":"1405.0827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0827","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0827v1","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0827","created_at":"2026-05-18T02:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"J4B37JBNKMD2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J4B37JBNKMD22EB3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J4B37JBN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:2af2f9ff58207c6de6b23d20eb38f61e23ca977836dac6d7a8e369f1dbc4f02a","target":"graph","created_at":"2026-05-18T02:52:40Z","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"},"paper":{"abstract_excerpt":"Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by N. Gigli and C. Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between non-linear sigma m","authors_text":"Mauro Carfora","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-05T08:54:22Z","title":"The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0827","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":"sha256:3d1dcc5fe05b81cc90da0f00a95d3b1c0fb04ad08edf078cb6e19b94f7bc7537","target":"record","created_at":"2026-05-18T02:52:40Z","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":"adaf4f53248311691c8f894e815090e9273b8c8a2fdce5db4d38822e6cc5febf","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-05T08:54:22Z","title_canon_sha256":"f255122dc06deaa1f18a4a1ac4aa490bcf7d56a65f9ce9068f38d8f26b242b58"},"schema_version":"1.0","source":{"id":"1405.0827","kind":"arxiv","version":1}},"canonical_sha256":"4f03bfa42d5307ad103b534a486b18d16eb9faa2758ae44f29309eb0e2d7ab40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f03bfa42d5307ad103b534a486b18d16eb9faa2758ae44f29309eb0e2d7ab40","first_computed_at":"2026-05-18T02:52:40.583794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:40.583794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TsUd19yfUk48l2f40AUspUeAxcbRfrNQcyxZHRrepx6NKlwWaYsZvCowW7VkdF0SXPzqe4iR2ejfxAnwJseCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:40.584207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1dcc5fe05b81cc90da0f00a95d3b1c0fb04ad08edf078cb6e19b94f7bc7537","sha256:2af2f9ff58207c6de6b23d20eb38f61e23ca977836dac6d7a8e369f1dbc4f02a"],"state_sha256":"0e5a02fbdbd08e4a9948ffd8389ea89f586a11423744508db24accc251149105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKR5JB/KhuOIJyz0PLFm8MqEnwUj10VsuZ+CnaiEql1+PoSFwZJ9SeFFs7ZIXKHsh43JKSzWOapZSfJnysgFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:04:39.620161Z","bundle_sha256":"73c7707988d0635a721b0ff985f50048823e0fc2508e19e6313b978513322e2b"}}