{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:27W2UZDPYH2SRKHF7BJ4Z5LLUL","short_pith_number":"pith:27W2UZDP","canonical_record":{"source":{"id":"1503.07663","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-26T09:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"82fa1ec491adb915dda59c3ff2bdbc2539a460b740a687813237df0882efda73","abstract_canon_sha256":"8c6b9700e7f19608b95e16941dbc58cf006ebb63faf13ff1d5d10dca67cd8368"},"schema_version":"1.0"},"canonical_sha256":"d7edaa646fc1f528a8e5f853ccf56ba2d7f0bc85ce9c612cf1301aa1a0cd4351","source":{"kind":"arxiv","id":"1503.07663","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07663","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07663v4","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07663","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"27W2UZDPYH2S","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"27W2UZDPYH2SRKHF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"27W2UZDP","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:27W2UZDPYH2SRKHF7BJ4Z5LLUL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.07663","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-26T09:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"82fa1ec491adb915dda59c3ff2bdbc2539a460b740a687813237df0882efda73","abstract_canon_sha256":"8c6b9700e7f19608b95e16941dbc58cf006ebb63faf13ff1d5d10dca67cd8368"},"schema_version":"1.0"},"canonical_sha256":"d7edaa646fc1f528a8e5f853ccf56ba2d7f0bc85ce9c612cf1301aa1a0cd4351","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:54.687730Z","signature_b64":"5Jnx25YmPLAomjzhPWT5Qzb9Sa2+glo2Tyk8AiU+Hy5uJaUIHizIbkXBzdQuBeA3TCtM5HH8c5RY+Z1sMPLQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7edaa646fc1f528a8e5f853ccf56ba2d7f0bc85ce9c612cf1301aa1a0cd4351","last_reissued_at":"2026-05-18T02:03:54.687218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:54.687218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.07663","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tcfAKMGce9KXnnLPdR3xwHk+RelD2m4gMxZTvPWdmDxRU4tbWU4BivkXy0fkhk2cW3PXINldQaLw8ZXk2sEeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:58:10.061463Z"},"content_sha256":"fe6955f633352207b6941ea04d5aa1c6cc80041597f0904a6429fad0e9b7894b","schema_version":"1.0","event_id":"sha256:fe6955f633352207b6941ea04d5aa1c6cc80041597f0904a6429fad0e9b7894b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:27W2UZDPYH2SRKHF7BJ4Z5LLUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Planck law for particle with rest mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Piero Chiarelli","submitted_at":"2015-03-26T09:49:51Z","abstract_excerpt":"In this work the author derives the Plank law for particles with rest mass that in the limit of photons with null rest mass leads to the known Plank law for the black body radiation. The paper shows that the relation has a pure quantum origin deriving it from the quantum potential of the hydrodynamic model. The paper puts under light how these laws originates by the scale invariance breaking due to the quantum potential. The paper also briefly analyzes the consequences of this symmetry breaking on the small-size black holes formation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07663","kind":"arxiv","version":4},"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":"2026-05-18T02:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRG8h8cY1K6oQM7CZeub5QdFhB0IRVqVXqTcmwMSUzSG27kJxZCCIsfVJYfVH/eoWob0m3E0g0Fa3cwZIsJGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:58:10.062099Z"},"content_sha256":"f2d6ea300effc78accc4ad058b250a6ca6050f746c139cd9e6c071a50702e8a4","schema_version":"1.0","event_id":"sha256:f2d6ea300effc78accc4ad058b250a6ca6050f746c139cd9e6c071a50702e8a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/bundle.json","state_url":"https://pith.science/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/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":"2026-06-06T13:58:10Z","links":{"resolver":"https://pith.science/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL","bundle":"https://pith.science/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/bundle.json","state":"https://pith.science/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27W2UZDPYH2SRKHF7BJ4Z5LLUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:27W2UZDPYH2SRKHF7BJ4Z5LLUL","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":"8c6b9700e7f19608b95e16941dbc58cf006ebb63faf13ff1d5d10dca67cd8368","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-26T09:49:51Z","title_canon_sha256":"82fa1ec491adb915dda59c3ff2bdbc2539a460b740a687813237df0882efda73"},"schema_version":"1.0","source":{"id":"1503.07663","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07663","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07663v4","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07663","created_at":"2026-05-18T02:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"27W2UZDPYH2S","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"27W2UZDPYH2SRKHF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"27W2UZDP","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f2d6ea300effc78accc4ad058b250a6ca6050f746c139cd9e6c071a50702e8a4","target":"graph","created_at":"2026-05-18T02:03:54Z","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":"In this work the author derives the Plank law for particles with rest mass that in the limit of photons with null rest mass leads to the known Plank law for the black body radiation. The paper shows that the relation has a pure quantum origin deriving it from the quantum potential of the hydrodynamic model. The paper puts under light how these laws originates by the scale invariance breaking due to the quantum potential. The paper also briefly analyzes the consequences of this symmetry breaking on the small-size black holes formation.","authors_text":"Piero Chiarelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-26T09:49:51Z","title":"The Planck law for particle with rest mass"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07663","kind":"arxiv","version":4},"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:fe6955f633352207b6941ea04d5aa1c6cc80041597f0904a6429fad0e9b7894b","target":"record","created_at":"2026-05-18T02:03:54Z","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":"8c6b9700e7f19608b95e16941dbc58cf006ebb63faf13ff1d5d10dca67cd8368","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-26T09:49:51Z","title_canon_sha256":"82fa1ec491adb915dda59c3ff2bdbc2539a460b740a687813237df0882efda73"},"schema_version":"1.0","source":{"id":"1503.07663","kind":"arxiv","version":4}},"canonical_sha256":"d7edaa646fc1f528a8e5f853ccf56ba2d7f0bc85ce9c612cf1301aa1a0cd4351","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7edaa646fc1f528a8e5f853ccf56ba2d7f0bc85ce9c612cf1301aa1a0cd4351","first_computed_at":"2026-05-18T02:03:54.687218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:54.687218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Jnx25YmPLAomjzhPWT5Qzb9Sa2+glo2Tyk8AiU+Hy5uJaUIHizIbkXBzdQuBeA3TCtM5HH8c5RY+Z1sMPLQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:54.687730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07663","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe6955f633352207b6941ea04d5aa1c6cc80041597f0904a6429fad0e9b7894b","sha256:f2d6ea300effc78accc4ad058b250a6ca6050f746c139cd9e6c071a50702e8a4"],"state_sha256":"c3e8c43429becd8ad77a0e277b4b8c9372f7cfa9c95be97dd010edf8c118d932"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQlDEILriWpl/xSUlTkY31gHeKqKJtCM7Z7FAy3TixVDoR3aGS1pB9+OUImw5oh0ThbWLlCq4S0qsWnTeDgBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:58:10.065807Z","bundle_sha256":"44730def7196cfc51ed4655aa640d49f2acb54b14a5eb1d686d9764b14ee7d14"}}